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Exhibit 10.1

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1 CONFIDENTIAL SETTLEMENT AGREEMENT AND RELEASE This Settlement Agreement and Release (“Agreement”), dated October 31, 2025, is entered into between Plaintiff Odeon Capital Group LLC (“Odeon” or “Plaintiff”) and Defendant AEON Biopharma, Inc. (“AEON”) (collectively with Odeon referred to as the “Parties”). RECITALS WHEREAS, on September 18, 2023, Plaintiff filed its Complaint in the Supreme Court of New York, New York County, in the litigation captioned Odeon Capital Group LLC v. AEON Biopharma, Inc., formerly known as Priveterra Acquisition Corp., and Continental Stock Transfer & Trust Company, bearing Index Number 654547/2023 (the “Action”); and WHEREAS, the Parties desire to avoid the costs and uncertainty of further litigation and agree to settle and resolve, completely and finally, all differences between Plaintiff and AEON, as well as between Plaintiff and Continental Stock Transfer & Trust Company (“Continental”), and all persons or entities released by this Agreement, without any admission of liability. This includes, without limitation, a desire to resolve completely and finally all claims made and raised by Plaintiff in the Action, against both AEON and Continental; and WHEREAS, the Parties were represented by counsel throughout the Action and during all settlement negotiations which resulted in the settlement of the Action and formulation of this Agreement; and NOW, THEREFORE, in consideration of the sum as outlined below (the “Consideration”) and other good and fair consideration, the Parties have reached a full and final compromise and settlement of any and all matters in controversy, disputes, causes of action, claims, contentions, and differences between them, and between Plaintiff and Continental, and hereby agree and understand as follows:

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2 1. Mutual Release of the Parties and Release of Continental. Plaintiff, AEON, and Continental individually and on behalf of themselves, their beneficiaries, heirs, administrators, representatives, executors, children, successors and assigns hereby knowingly and voluntarily releases, acquits, and forever discharges the other individually and on behalf of their present and former subsidiaries, affiliates, members, managers, directors, officers, employees, agents, advisors, consultants, representatives, shareholders, insurers and attorneys, and their heirs, successors, and assigns (whether or not acting within the scope of their duties) from all claims of any nature whatsoever which Plaintiff, AEON or Continental now has or asserts to have, or which Plaintiff, AEON, or Continental at any time heretofore had, or asserted to have against the other arising out of or in any way related in any way to any acts, circumstances, facts, transactions, omissions or other subject matters, based on facts occurring prior to the date of this Agreement. Plaintiff, AEON, and Continental specifically releases the following claims: Any and all past, present or future claims, demands, obligations, actions, causes of action, rights, damages, costs, loss of services, expenses, and compensation of any nature whatsoever based on a tort, contract, or other theory of recovery, and whether for compensatory or punitive damages Plaintiff, AEON, or Continental may now have, or which may hereafter accrue or otherwise be acquired against the other’s agents, servants and employees directly or indirectly, including by way of example those which may be or could have been the subject matter of a lawsuit pending in the Supreme Court of New York, New York County, in the Action captioned Odeon Capital Group LLC v. AEON Biopharma, Inc., formerly known as Priveterra Acquisition Corp., and Continental Stock Transfer & Trust Company, bearing the Index Number 654547/2023. This Mutual Release is for compensation of any and all injuries Plaintiff, AEON or Continental has sustained, known or unknown, or unknowable related to the claims asserted in the Action. It is expressly understood that this Mutual Release is for the settlement, release, discharge, and elimination of any and all such

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3 claims. Plaintiff, AEON, and Continental hereby acknowledge that by executing this Mutual Release and accepting the consideration paid hereunder Plaintiff, AEON, Continental and those who otherwise might be entitled to make such a claim or claims in the future has received fair, just and adequate compensation for all such claims in exchange for which all such claims, past, present and future are forever released and discharged. Even if additional facts become known which were not known at the time this Release was executed, Plaintiff, AEON, and Continental waives its right to bring a lawsuit against the other for any injuries alleged to have been caused due to the actions and conduct alleged in the Complaint filed by Plaintiff in the Action. Nothing herein shall release (i) obligations under this Agreement; (ii) any rights or obligations arising after the Effective Date; or (iii) claims for breach of this agreement. 2. Dismissal of Action. Plaintiff will file a Stipulation of Discontinuance of the Action, with prejudice, within five (5) days of receipt of the Consideration as set forth in Section 3 of this Agreement. This Agreement is expressly conditioned upon full and proper execution of the Stipulation for Discontinuance and the filing thereof. 3. Consideration. In consideration for Plaintiff making the Release as set forth above, and other good and fair consideration, AEON agrees to (i) pay Plaintiff the sum of $1,000,000 (ONE MILLION DOLLARS AND ZERO CENTS) payable to Odeon Capital Group LLC; (ii) transfer to Odeon shares of AEON Class A common stock equal to U.S.$250,000 based on a weighted volume average price for the five trading days immediately following the execution of this Agreement, subject to a $0.50 per share floor; and (iii) issue to Odeon a Warrant to Purchase up to 125,000 shares of AEON’s Class A common stock, with said form and terms of such Warrants as set forth on Exhibit A hereto. The Consideration set forth above shall be delivered within twenty (20) days of the full execution of this Agreement, and receipt by AEON of wire instructions and a W-9. For the avoidance

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4 of doubt, Continental is not undertaking any obligation regarding the settlement, other than as expressly set forth in the Agreement. 4. Representations and Warranties. (a) Plaintiff and AEON represent and warrant that they have the full right, power and authority to execute, deliver and perform this Settlement Agreement. (b) Plaintiff and AEON represent and warrant that their signatory has the full authority to enter into this Settlement Agreement and bind the party that it represents. (c) Plaintiff and AEON represent and warrant that they are relying on their own counsel and advice that each has received from its attorneys in executing this Settlement Agreement. (d) Plaintiff acknowledges and agrees that any shares of AEON Class A common stock issued pursuant to the Agreement (the “Settlement Shares”) are subject to a resale limitations such that Odeon shall not, directly or indirectly, sell, transfer, or otherwise dispose of, in any public or private transaction, shares of AEON Class A common stock in any calendar week in an amount exceeding ten percent (10%) of the total number of Settlement Shares originally issued to Odeon hereunder (the “Weekly Limit”). Sales or transfers in violation of this provision shall be null and void and of no effect, and AEON shall be entitled to take all necessary actions to prevent or reverse any such sale, including instructing its transfer agent to decline to process or record any transfer inconsistent with the Weekly Limit or seeking injunctive relief. (e) Plaintiff agrees not to perfect any appeal relating to or arising from the Action against Continental. 5. Bound Parties. The Parties are bound by this Settlement and Release. This Agreement shall be binding upon and the benefits shall inure to AEON and their respective successors and assigns, as well as to Plaintiff and Plaintiff’s successors, assigns and representatives.

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5 6. Entire Agreement. The Parties agree that this Agreement constitutes the entire agreement between the Parties and that any amendment must be in writing and executed by both parties. 7. Notices. All notices, demands, requests, consents, approvals, or other communications required or permitted under this Agreement (“Notices”) shall be in writing and shall be deemed duly given and effective upon delivery by email or overnight courier service. Notices shall be directed to each Party’s respective litigation counsel of record in the Action, and delivery to such counsel shall constitute valid and effective notice to that Party. 8. Tax Treatment. Each Party shall be solely responsible for any and all taxes, assessments, or other liabilities that may be imposed on it arising out of or relating to the Consideration provided under this Agreement. AEON shall have no obligation to withhold, collect, or remit any taxes on behalf of Plaintiff, and Plaintiff agrees to indemnify and hold AEON harmless from and against any claim, liability, penalty, or expense (including reasonable attorneys’ fees) arising from or relating to any such taxes. The Parties acknowledge and agree that no portion of the Consideration constitutes wages, salary, or other compensation for services rendered, and that Plaintiff has not relied on AEON for any tax advice in connection with this Agreement. Plaintiff further represents that it has consulted with its own tax advisors regarding the tax consequences of this settlement. 9. Disclaimer of Liability. The Parties acknowledge and agree that the execution of this Agreement shall not be considered an admission of liability or of responsibility by AEON concerning any of the claims referred to herein, and no past or present wrongdoing on the part of any of the Parties to this Agreement shall be implied by such payment or execution. 10. Nonadmissibility. This Agreement shall not be admissible in any legal proceeding except to the extent Court approval of the settlement is required or to enforce the terms of the Agreement. nor shall the terms herein prejudice any party hereto in any other proceeding.

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6 11. Representation/Authority. The Parties acknowledge that they have been represented in negotiations for, and in the preparation of, this Agreement by counsel of their choosing. The Parties represent that they have read this Agreement, know and understand the terms of this Agreement and its legal effect, that they have executed it voluntarily, that they have not been influenced by any persons or other parties, and that they have authority to sign this Agreement. Accordingly, the Parties expressly agree that any rule of law, including, but not limited to, the doctrine of contra proferentum, or any legal decision that would require a legal interpretation of any claimed ambiguities in this Agreement against the party that drafted it, has no application. 12. Partial Invalidity. If any term or provision of this Agreement is held by any court of competent jurisdiction to be invalid or unenforceable, such invalidity or unenforceability shall not invalidate the total Agreement. Instead, this Agreement shall be construed as if it did not contain such term or provision, and the remainder of this Agreement shall remain in full force and effect. 13. Choice of Law, Venue, and Waiver of Jury Trial. The Parties agree that this Agreement shall be interpreted, enforced and governed by the laws of the State of New York and that any dispute concerning this agreement shall be brought in the New York Supreme Court, New York County. 14. Counterparts. This Agreement may be executed in counterparts, each of which when so executed shall be deemed to be an original, and such counterparts together shall constitute one and the same Agreement. A faxed or electronically transmitted signature shall bear the same force and effect as an original signature. The Parties nevertheless expressly agree that they will promptly provide the other with a duly signed copy of this Agreement bearing the original signature of such respective party. THE PARTIES REPRESENT THAT THEY FULLY UNDERSTAND THEIR RIGHT TO DISCUSS ALL ASPECTS OF THIS AGREEMENT WITH THEIR PRIVATE ATTORNEYS AND THAT THEY HAVE, PRIOR TO EXECUTING THIS DOCUMENT, FULLY INFORMED THEMSELVES OF ITS CONTENTS THROUGH ATTORNEYS, ADVISORS AND/OR

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7 SOURCES OF THEIR OWN SELECTION. THE PARTIES ALSO REPRESENT THAT THEY HAVE CAREFULLY READ AND FULLY UNDERSTAND ALL THE PROVISIONS OF THIS AGREEMENT AND ARE VOLUNTARILY ENTERING INTO THIS AGREEMENT. EACH PERSON SIGNING BELOW ON BEHALF OF ANY ENTITY HEREBY PERSONALLY AND EXPRESSLY REPRESENTS AND WARRANTS THAT HE OR SHE IS SIGNING ON BEHALF OF SUCH ENTITY WITH FULL LEGAL AUTHORITY TO BIND SUCH PARTY TO EACH AND EVERY PROVISION OF THIS AGREEMENT: Odeon Capital Group LLC, Dated: Print Name AEON Biopharma, Inc. Dated: By: Robert Bancroft CEO & President Continental Stock Transfer & Trust Company* *As to Mutual Release Only Dated: Print Name /s/ Evan Schwartzbert Evan Schwartzbert, CEO 10/31/2025 /s/ Robert Bancroft 11/5/2025 Steven G. Nelson 10/31/2025 /s/ Steven G. Nelson