Exhibit 1.1

November 28, 2018

Kosmos Energy Ltd.

Clarendon House 

2 Church Street

Hamilton HM 11, Bermuda

Ladies and Gentlemen:

Reference is made to the Shareholders Agreement, dated as of May 10, 2011 (the “Shareholders Agreement”), by and among Kosmos Energy Ltd., an exempted company incorporated under the laws of Bermuda (the “Company”), and each of the parties identified on Schedule A to the Shareholders Agreement. Capitalized or other terms used and not defined herein but defined in the Shareholders Agreement shall have the meanings ascribed to them in the Shareholders Agreement.

The undersigned hereby irrevocably waive (a) their rights pursuant to Section 2.1 of the Shareholders Agreement to nominate and/or designate persons to the Board and (b) their rights pursuant to Section 2.2 of the Shareholders Agreement to nominate and/or designate persons to committees of the Board.

Further, the undersigned hereby irrevocably waive (a) their rights pursuant to Section 2.1 of Annex A to the Company’s Bye-Laws to nominate and/or designate persons to the Board and (b) their rights pursuant to Section 2.2 of Annex A to the Company’s Bye-Laws to nominate and/or designate persons to committees of the Board.

The undersigned hereby further agree that, with respect to all Common Shares collectively held by them in excess of 9.99% of the outstanding Common Shares of the Company at the time in question (such shares, “Excess Shares”), the undersigned shall vote or cause to be voted at all meetings of the shareholders of the Company, or vote, consent or approve in any other circumstances, upon which such vote, consent or other approval (including a written consent) is sought or obtained by or from the shareholders of the Company, all Excess Shares in the same manner (including by voting “for” or “against,” abstaining or withholding votes) as, and in the same proportion to, the votes cast “for” or “against,” and abstentions or vote withholdings made, in respect of all Common Shares held by holders of Common Shares (other than the Common Shares held by the undersigned).

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Accepted and agreed as of the date first written above.