REDEMPTION AGREEMENT

Exhibit 10.10

REDEMPTION AGREEMENT

This Agreement (the “Agreement”) is made as of March 6, 2015, by and among Zeta Acquisition Corp. III, a Delaware corporation (the “Issuer”), and the stockholders of the Issuer listed on Schedule A attached hereto (collectively, the “Sellers”).

WITNESSETH:

WHEREAS, the Sellers are the owner of 5,000,000 shares of the Issuer’s common stock, par value $0.0001 per share (“Common Stock”) as set forth on Schedule A hereto; and

WHEREAS, the Sellers desire to sell to the Issuer, severally and not jointly, and the Issuer desires to re-purchase and redeem from the Sellers, the number of shares of Common Stock listed on Schedule A set forth opposite such Seller’s name, which shall result in the re-purchase and redemption by the Issuer of an aggregate of 5,000,000 shares of Common Stock (the “Shares”), on and subject to the terms of this Agreement.

WHEREFORE, the parties hereto hereby agree as follows:

1. Sale of the Shares. Subject to the terms and conditions of this Agreement, and in reliance upon the representations, warranties, covenants and agreements contained in this Agreement, the Sellers shall sell to the Issuer the number of Shares listed on Schedule A set forth opposite each Seller’s name, and the Issuer shall re-purchase and redeem such Shares from the Sellers, for an aggregate purchase price equal to the sum of seventy thousand dollars ($70,000) (the “Purchase Price”). The Sellers shall be entitled to that portion of the Purchase Price listed on Schedule A set forth opposite such Seller’s name.

2. Closing.

(a) The purchase and sale of the Shares shall take place at a closing (the “Closing”), to occur immediately following the effectiveness of the merger transaction (the “Merger”) contemplated by that certain Agreement and Plan of Merger, dated March 6, 2015 (the “Merger Agreement”; capitalized terms used but not specifically defined herein shall have the meanings ascribed to such terms in the Merger Agreement) among the Issuer, Kura Oncology, Inc. (“Kura”), and Kura Operations, Inc. (“Merger Sub”), a wholly-owned subsidiary of the Issuer. The parties hereto shall have no obligation to complete the Closing in the event the Merger is not consummated.

(b) At the Closing:

(i) Each of the Sellers shall deliver to the Issuer an irrevocable stock power in the form attached hereto on Exhibit A representing such Seller’s portion of the Shares, duly endorsed in form for transfer to the Issuer.

(ii) The Issuer shall pay to each Seller that portion of the Purchase Price listed on Schedule A set forth opposite such Seller’s name.

(iii) At, and at any time after, the Closing, the Sellers shall duly execute, acknowledge and deliver all such further assignments, conveyances, instruments and documents, and shall take such other action consistent with the terms of this Agreement to carry out the transactions contemplated by this Agreement, as may be requested by the Issuer.

(c) Repurchased Shares Cancelled. Immediately upon the Closing, the Shares shall be cancelled and shall lose all previously applicable rights, preferences and privileges (including, but not limited to, any and all shareholder and voting rights).

3. Representations and Warranties of each Seller. Each Seller makes the following representations and warranties to the Issuer with respect to such Seller and the Shares to be sold by such Seller hereunder:

(a) Seller is a citizen of the United States of America.

(b) Seller is an “accredited investor” as such term is defined in Rule 501(a) of Regulation D promulgated under the Securities Act.

(c) Seller has the requisite power and authority to enter into this Agreement and to consummate the transactions contemplated hereby and otherwise to carry out its obligations hereunder.

(d) Seller is the record and sole beneficial owner of the number of Shares listed on Schedule A set forth opposite Seller’s name and has good and marketable title to the Shares, free and clear of any and all options, liens, claims, encumbrances, security interests, pledges, preemptive rights, rights of first refusal and adverse interests of any kind. Seller agrees that the consideration payable by the Issuer for the re-purchase and redemption of Seller’s Shares is fair and reasonable and that Seller is in the best position to evaluate and determine the fair value of such Shares. There are no restrictions on the transfer or redemption of such Shares (other than restrictions under the Securities Act or state securities laws). No person or entity (i) owns any equity interest in the Issuer other than the Seller, or (ii) has any right to purchase Seller’s Shares or any portion thereof or interest therein.

(e) Seller has received and reviewed the Merger Agreement and understands and consents to the transactions contemplated thereby. Seller has been afforded the opportunity during the course of negotiating the transactions contemplated by this Agreement to ask questions of, and to secure such information from, the Issuer and its officers and directors with regard to the Issuer, Kura and Merger Sub as it deems necessary to evaluate the merits of consenting to the Issuer’s consummating such transactions, it being understood that Seller is a stockholder and an affiliate of a director of the Issuer and, as such, is intimately familiar with the Issuer and its business, operations, assets, liabilities, prospects and financial condition in all respects. All such questions, if asked, were answered satisfactorily and all information or documents provided were found to be satisfactory.

(f) There is no private or governmental action, suit, proceeding, claim, arbitration or investigation pending before any agency, court or tribunal, foreign or domestic, or, to Seller’s knowledge, threatened against the Seller or any of their properties. There is no judgment, decree or order against the Seller that could prevent, enjoin, alter or delay any of the transactions contemplated by this Agreement. No bankruptcy, receivership or debtor relief proceedings are pending or, to Seller’s knowledge, threatened against the Seller.

(g) All representations, covenants and warranties of the Seller contained in this Agreement shall be true and correct on and as of the Closing Date with the same effect as though the same had been made on and as of such date.

4. Termination by Mutual Agreement. This Agreement may be terminated at any time by mutual consent of the parties hereto, provided that such consent to terminate is in writing and is signed by each of the parties hereto.

5. Release. Each Seller, on its own behalf and, to the extent of its legal authority, on behalf of its successors, assigns, heirs, next-of-kin, representatives, administrators, executors, partners, agents and affiliates, and any other person claiming by, through, or under any of the foregoing (individually, a “Releasing Party” and collectively, “Releasing Parties”), hereby unconditionally and irrevocably releases, waives and forever discharges, effective as of the Closing, the Issuer and Kura, and each of their past and present respective officers, directors, employees, stockholders, predecessors, successors, assigns, partners, subsidiaries and affiliates (individually, a “Released Party” and collectively, “Released Parties”) from any and all claims, obligations, contracts, agreements, rights, debts, covenants and liabilities (including attorneys’ fees and costs) of any nature whatsoever, whether fixed or contingent, known or unknown, suspected or claimed to exist or unsuspected, regardless of whether knowledge of the unknown or unsuspected claim would have materially affected such Seller’s decision to enter into this Agreement, both at law and in equity, arising directly or indirectly from any act, omission, event, or transaction occurring (or any facts or circumstances existing) on or prior to the Closing, but excluding (i) claims for breach by the Issuer of any provision of this Agreement, and (ii) the rights of John Pappajohn and Matthew P. Kinley under the Indemnity Agreement, including their respective indemnification rights thereunder.

6. Miscellaneous.

(a) Entire Agreement. This Agreement constitutes the entire agreement of the parties, superseding and terminating any and all prior or contemporaneous oral and written agreements, understandings or letters of intent between or among the parties, with respect to the subject matter of this Agreement. No part of this Agreement may be modified or amended, nor may any right be waived, except by a written instrument which expressly refers to this Agreement, states that it is a modification or amendment of this Agreement and is signed by the parties to this Agreement, or, in the case of waiver, by the party granting the waiver. No course of conduct or dealing or trade usage or custom and no course of performance shall be relied on or referred to by any party to contradict, explain or supplement any provision of this Agreement, it being acknowledged by the parties to this Agreement that this Agreement is intended to be, and is, the complete and exclusive statement of the agreement with respect to its subject matter. Any waiver shall be limited to the express terms thereof and shall not be construed as a waiver of any other provisions or the same provisions at any other time or under any other circumstances.

(b) Severability. If any section, term or provision of this Agreement shall to any extent be held or determined to be invalid or unenforceable, the remaining sections, terms and provisions shall nevertheless continue in full force and effect.

(c) Notices. All notices provided for in this Agreement shall be in writing signed by the party giving such notice, and delivered personally or sent by overnight courier, mail or messenger against receipt thereof or sent by registered or certified mail, return receipt requested, or by facsimile transmission or similar means of communication if receipt is confirmed or if transmission of such notice is confirmed by mail as provided in this Section6(c). Notices shall be deemed to have been received on the date of personal delivery or telecopy or attempted delivery. Notice shall be delivered to the parties at the following addresses:

If to the Issuer (on or before the Closing):

Either party may, by like notice, change the address, person or facsimile number to which notice shall be sent.

(d) Governing Law. This Agreement shall be governed and construed in accordance with the laws of the State of New York applicable to agreements executed and to be performed wholly within such State, without regard to any principles of conflicts of law. Each of the parties hereby irrevocably consents and agrees that any legal or equitable action or proceeding arising under or in connection with this Agreement shall be brought in the federal or state courts located in the County of New York in the State of New York, by execution and delivery of this Agreement, irrevocably submits to and accepts the jurisdiction of said courts, waives any defense that such court is not a convenient forum, and consents to any service of process made either (x) in the manner set forth in Section 6(c) of this Agreement (other than by telecopier), or (y) any other method of service permitted by law.

(e) Waiver of Jury Trial. EACH PARTY HEREBY EXPRESSLY WAIVES ANY RIGHT TO A TRIAL BY JURY IN THE EVENT OF ANY SUIT, ACTION OR PROCEEDING TO ENFORCE THIS AGREEMENT OR ANY OTHER ACTION OR PROCEEDING WHICH MAY ARISE OUT OF OR IN ANY WAY BE CONNECTED WITH THIS AGREEMENT OR ANY OF THE OTHER DOCUMENTS.

(f) Successors. This Agreement shall be binding upon the parties and their respective heirs, executors, administrators, legal representatives, successors and assigns; provided, however, that neither party may assign this Agreement or any of its rights under this Agreement without the prior written

consent of the other party.

(g) Further Assurances. Each party to this Agreement agrees, without cost or expense to any other party, to deliver or cause to be delivered such other documents and instruments as may be reasonably requested by any other party to this Agreement in order to carry out more fully the provisions of, and to consummate the transaction contemplated by, this Agreement.

(h) Counterparts. This Agreement may be executed simultaneously in two or more counterparts, each of which shall be deemed an original but all of which together shall constitute one and the same instrument. This Agreement and any documents relating to it may be executed and transmitted to any other party by facsimile or email of a PDF, which facsimile or PDF shall be deemed to be, and utilized in all respects as, an original, wet-inked document.

(i) No Strict Construction. The language used in this Agreement will be deemed to be the language chosen by the parties with the advice of counsel to express their mutual intent, and no rules of strict construction will be applied against any party.

(j) Survival of Representations and Warranties. All representations and warranties made by the Seller in this Agreement shall survive the execution and delivery hereof and any investigations made by or on behalf of the parties.

(k) Headings. The headings in the Sections of this Agreement are inserted for convenience only and shall not constitute a part of this Agreement.

(l) Specific Performance. The rights and remedies of the parties hereto shall be cumulative. The transactions contemplated by this Agreement are unique transactions and any failure on the part of any party to complete the transactions contemplated by this Agreement on the terms of this Agreement will not be fully compensable in damages and the breach or threatened breach of the provisions of this Agreement would cause the other parties hereto irreparable harm. Accordingly, in addition to and not in limitation of any other remedies available to the parties hereto for a breach or threatened breach of this Agreement, the parties shall be entitled to seek specific performance of this Agreement and seek an injunction restraining any such party from such breach or threatened breach.

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed as of the date first above written.

[Signature Page to Redemption Agreement]

SCHEDULE A

EXHIBIT A

IRREVOCABLE STOCK POWER

FOR VALUE RECEIVED, the undersigned does hereby sell, assign and transfer to Zeta Acquisition Corp. III, a Delaware corporation (the “Corporation”), [            ] ([            ]) shares of the Common Stock, $0.0001 par value per share, of the Corporation, standing in the name of the undersigned on the books of the Corporation. The undersigned does hereby irrevocably constitute and appoint              as attorney to transfer the said shares on the books of the Corporation, with full power of substitution in the premises. This Irrevocable Stock Power is given pursuant to a Redemption Agreement dated as of March 6, 2015 and is subject to the terms of that agreement.