Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement (Form S-8) pertaining to the Kura Oncology, Inc. Amended and Restated 2014 Equity Incentive Plan of our report dated March 5, 2019, with respect to the financial statements of Kura Oncology, Inc. included in its Annual Report (Form 10-K) for the year ended December 31, 2018, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

San Diego, California

March 5, 2019