ALPAU Alpha Healthcare Acquisition Corporation III

Business Combination Agreement

On January 4, 2023, Alpha Healthcare Acquisition Corp. III, a Delaware corporation (the “Company”), entered into a business combination agreement (the “Business Combination Agreement”) by and among the Company, Candy Merger Sub, Inc., a Delaware corporation (“Merger Sub”), and Carmell Therapeutics Corporation, a Delaware corporation (“Carmell”). The Business Combination Agreement provides, among other things, that on the terms and subject to the conditions set forth therein, Merger Sub will merge with and into Carmell, with Carmell surviving as a wholly-owned subsidiary of the Company (the “Business Combination”). Upon the closing of the Business Combination (the “Closing”), it is anticipated that the Company will change its name to “Carmell Therapeutics Corporation.” The date on which the Closing actually occurs is hereinafter referred to as the “Closing Date.”

The Business Combination Agreement and the transactions contemplated thereby were approved by the boards of directors of each of the Company and Carmell.

Consideration and Structure

Under the Business Combination Agreement, the Company will acquire all of the outstanding equity interests of Carmell in exchange for shares of the Company’s Class A common stock, par value $0.0001 per share (the “Class A Common Stock”), based on an implied Carmell equity value of $150,000,000, to be paid to Carmell stockholders at the effective time of the Business Combination.

Pursuant to the Business Combination Agreement, at or prior to the effective time of the Business Combination, each option and warrant exercisable for Carmell equity that is outstanding immediately prior to the effective time of the Business Combination shall be assumed by the Company and continue in full force and effect on the same terms and conditions as are currently applicable to such options and warrants, subject to adjustments to exercise price and number of shares of Class A Common Stock issued upon exercise.

Representations, Warranties and Covenants

The parties to the Business Combination Agreement have agreed to customary representations and warranties for transactions of this type. In addition, the parties to the Business Combination Agreement agreed to be bound by certain customary covenants for transactions of this type, including, among others, covenants with respect to the conduct of Carmell, the Company and their respective subsidiaries during the period between execution of the Business Combination Agreement and Closing. The representations, warranties, agreements and covenants of the parties set forth in the Business Combination Agreement will terminate at Closing, except for those covenants and agreements that, by their terms, contemplate performance after Closing. Each of the parties to the Business Combination Agreement has agreed to use its reasonable best efforts to take or cause to be taken all actions and things necessary to consummate and expeditiously implement the Business Combination.

Conditions to Closing

Under the Business Combination Agreement, the obligations of the parties to consummate the Business Combination are subject to the satisfaction or waiver of certain customary closing conditions of the respective parties, including, without limitation: (i) the approval and adoption of the Business Combination Agreement and transactions contemplated thereby by requisite vote of the Company’s stockholders (the “Company Stockholder Approval”) and Carmell’s stockholders (the “Carmell Stockholder Approval”); (ii) the execution of the Investor Rights Agreement (as defined below) by the parties thereto; (iii) the expiration or termination of the applicable waiting period under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended; (iv) the absence of a Company Material Adverse Effect or ALPA Material Adverse Effect (each, as defined in the Business Combination Agreement) since the date of the Business Combination Agreement that is continuing; (v) after giving effect to the transactions contemplated by the Business Combination Agreement, the Company has net tangible assets of at least $5,000,001 upon consummation of the Business Combination; (vi) the Company’s initial listing application with The Nasdaq Stock Market (“Nasdaq”) in connection with the Business Combination has been approved and, immediately following the effective time of the Business Combination, the Company has satisfied any applicable initial and continuing listing requirements of Nasdaq, and the Company has not received any notice of non-compliance therewith that has not been cured or would not be cured, and the shares of the Company’s Class A Common Stock have been approved for listing on Nasdaq; (vii) the S-4 Registration Statement (as defined below) has become effective, no stop order has been issued by the Securities and Exchange Commission (the “SEC”) and remains in effect with respect to the S-4 Registration

2/6

Statement, and no proceeding seeking such a stop order has been threatened or initiated by the SEC and remains pending; and (viii) Carmell shall have paid off all amounts due under the 10% Original Issue Discount Senior Secured Convertible Notes, dated as of January 19, 2023.

Termination

The Business Combination Agreement may be terminated under certain customary and limited circumstances at any time prior to the Closing, including, without limitation, (i) by the Company or Carmell, if (a) the Closing has not occurred by June 30, 2023 and (b) a breach of the covenants or obligations of the other party (Carmell, on one hand, or the Company or Merger Sub, on the other hand) seeking to terminate the Business Combination Agreement did not proximately cause the failure to consummate the Business Combination; (ii) by the Company or Carmell, in the event an applicable governmental, regulatory or administrative authority has issued a final and non-appealable order having the effect of permanently restraining, enjoining or otherwise prohibiting the Business Combination; (iii) by the Company or Carmell, if Carmell or the Company or Merger Sub, as applicable, has breached any of its respective representations, warranties, agreements or covenants contained in the Business Combination Agreement, such failure or breach would render certain conditions precedent to the Closing incapable of being satisfied, and such breach or failure is not cured within 30 days of written notice thereof; (iv) by the Company or Carmell if the Company’s stockholder meeting to vote on the Business Combination has been held and the Company Stockholder Approval has not been obtained; (v) by the Company, if the Carmell Stockholder Approval is not obtained within five (5) business days following the time at which a registration statement on Form S-4 (the “S-4 Registration Statement”) relating to the approval by the Company’s stockholders of the Business Combination filed with the SEC by the Company is declared effective under the Securities Act of 1933, as amended (the “Securities Act”); or (vi) by mutual written consent of the Company and Carmell.

If the Business Combination Agreement is validly terminated, none of the parties to the Business Combination Agreement will have any liability or any further obligation under the Business Combination Agreement other than customary confidentiality obligations, except in the case of Willful Breach or Fraud (each, as defined in the Business Combination Agreement).

A copy of the Business Combination Agreement is filed with this Current Report on Form 8-K as Exhibit 2.1 and is incorporated herein by reference, and the foregoing description of the Business Combination Agreement and the Business Combination does not purport to be complete and is qualified in its entirety by reference thereto. The Business Combination Agreement contains representations, warranties and covenants that the respective parties made to each other as of the date of the Business Combination Agreement or other specific dates. The assertions embodied in those representations, warranties and covenants were made for purposes of the contract among the respective parties and are subject to important qualifications and limitations agreed to by the parties in connection with negotiating the Business Combination Agreement. The Business Combination Agreement is being filed to provide investors with information regarding its terms. It is not intended to provide any other factual information about the parties to the Business Combination Agreement. In particular, the representations, warranties, covenants and agreements contained in the Business Combination Agreement, which were made only for purposes of the Business Combination Agreement and as of specific dates, were solely for the benefit of the parties to the Business Combination Agreement, may be subject to limitations agreed upon by the contracting parties (including being qualified by confidential disclosures made for the purposes of allocating contractual risk between the parties to the Business Combination Agreement instead of establishing these matters as facts) and may be subject to standards of materiality applicable to the contracting parties that differ from those applicable to investors, security holders and reports and documents filed with the SEC. Investors and security holders are not third-party beneficiaries under the Business Combination Agreement and should not rely on the representations, warranties, covenants and agreements, or any descriptions thereof, as characterizations of the actual state of facts or condition of any party to the Business Combination Agreement. In addition, the representations, warranties, covenants and agreements and other terms of the Business Combination Agreement may be subject to subsequent waiver or modification.

The information in this Item 7.01 and Exhibits 99.1 and 99.2 attached hereto shall not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), or otherwise subject to the liabilities of that section, nor shall it be deemed incorporated by reference in any filing under the Securities Act or the Exchange Act, except as expressly set forth by specific reference in such filing.

Important Information About the Merger and Where to Find It

A full description of the terms of the Business Combination will be provided in the S-4 Registration Statement to be filed with the SEC by the Company, which will include a prospectus with respect to the Company’s securities to be issued in connection with the Business Combination and a proxy statement with respect to the stockholder meeting of the Company to vote on the Business Combination. The Company urges its investors, stockholders and other interested persons to read, when available, the preliminary proxy statement/prospectus as well as other documents filed with the SEC because these documents will contain important information about the Company, Carmell and the Business Combination. After the S-4 Registration Statement is declared effective, the definitive proxy statement/prospectus to be included in the registration statement will be mailed to stockholders of the Company as of a record date to be established for voting on the proposed Business Combination. Once available, stockholders will also be able to obtain a copy of the S-4 Registration Statement, including the proxy statement/prospectus, and other documents filed with the SEC without charge, by directing a request to: Alpha Healthcare Acquisition Corp. III, 1177 Avenue of the Americas, 5^th Floor, New York, New York 10036. The preliminary and definitive proxy statement/prospectus to be included in the S-4 Registration Statement, once available, can also be obtained, without charge, at the SEC’s website (www.sec.gov).

Participants in the Solicitation

The Company and Carmell and their respective directors and executive officers may be considered participants in the solicitation of proxies with respect to the proposed Business Combination described in this Current Report on Form 8-K under the rules of the SEC. Information about the directors and executive officers of the Company is set forth in the Company’s final prospectus filed with the SEC pursuant to Rule 424(b) of the Securities Act on July 27, 2021, and is available free of charge at the SEC’s website at www.sec.gov or by directing a request to: Alpha Healthcare Acquisition Corp. III, Attn: Secretary, 1177 Avenue of the Americas, 5^th Floor, New York, New York 10036. Information regarding the persons who may, under the rules of the SEC, be deemed participants in the solicitation of the Company’s stockholders in connection with the proposed Business Combination will be set forth in the registration statement containing the proxy statement/prospectus for the proposed Business Combination when it is filed with the SEC. These documents can be obtained free of charge from the sources indicated above.

Forward-Looking Statements

This Current Report contains forward-looking statements that are based on beliefs and assumptions and on information currently available. In some cases, you can identify forward-looking statements by the following words: “may,” “will,” “could,” “would,” “should,” “expect,” “intend,” “plan,” “anticipate,” “believe,” “estimate,” “predict,” “project,” “potential,” “continue,” “ongoing” or the negative of these terms or other comparable terminology, although not all forward-looking statements contain these words. These statements involve risks, uncertainties and other factors that may cause actual results, levels of activity, performance or achievements to be materially different from the information expressed or implied by these forward-looking statements. Although we believe that we have a reasonable basis for each forward-looking statement contained in this Current Report, we caution you that these statements are based on a combination of facts and factors currently known by us and our projections of the future, about which we cannot be certain. Forward-looking statements in this Current Report include, but are not limited to, statements regarding the proposed Business Combination, including the timing and structure of the Business Combination, the proceeds of the Business Combination, the initial market capitalization of the combined company following the Closing and the benefits of the Business Combination, as well as statements about the potential attributes and benefits of Carmell’s product candidates and the format and timing of Carmell’s product development activities and clinical trials. We cannot assure you that the forward-looking statements in this Current Report will prove to be accurate. These forward-looking statements are subject to a number of significant risks and uncertainties that could cause actual results to differ materially from expected results, including, among others, the ability to complete the Business Combination due to the failure to obtain approval from the Company’s stockholders or satisfy other closing conditions in the Business Combination Agreement, the occurrence of any event that could give rise to the termination of the Business Combination Agreement, the ability to recognize the anticipated benefits of the Business Combination, the outcome of any legal proceedings that may be instituted against the Company or Carmell following announcement of the proposed Business Combination and related transactions, the impact of current macroeconomic and geopolitical events, including changing conditions from the COVID-19 pandemic, the hostilities in Ukraine, increasing rates of inflation, rising interest rates and fluctuations in foreign exchange rates on Carmell’s business and/or the ability of the parties to complete the Business Combination, the ability to obtain or maintain the listing of the Company’s Class A Common Stock on Nasdaq following the proposed Business Combination, costs related to the proposed Business Combination, changes in applicable laws or regulations, the possibility that the Company or Carmell may be adversely affected by other economic, business, and/or competitive factors. and other risks and uncertainties, including those to be included under the header “Risk Factors”

4/6

in the S-4 Registration Statement to be filed by the Company with the SEC and those included under the header “Risk Factors” in the final prospectus of the Company related to its initial public offering. Most of these factors are outside the Company’s and Carmell’s control and are difficult to predict. Furthermore, if the forward-looking statements prove to be inaccurate, the inaccuracy may be material. In light of the significant uncertainties in these forward-looking statements, you should not regard these statements as a representation or warranty by us or any other person that we will achieve our objectives and plans in any specified time frame, or at all. The forward-looking statements in this Current Report represent our views as of the date of this Current Report. We anticipate that subsequent events and developments will cause our views to change. However, while we may elect to update these forward-looking statements at some point in the future, we have no current intention of doing so except to the extent required by applicable law. You should, therefore, not rely on these forward-looking statements as representing our views as of any date subsequent to the date of this Current Report.

No Offer or Solicitation

This Current Report is not a proxy statement or solicitation of a proxy, consent or authorization with respect to any securities or in respect of the proposed Business Combination and shall not constitute an offer to sell or a solicitation of an offer to buy any securities, nor shall there be any sale of securities in any state or jurisdiction in which such offer, solicitation, or sale would be unlawful prior to registration or qualification under the securities laws of such state or jurisdiction. No offer of securities shall be made except by means of a prospectus meeting the requirements of the Securities Act.