Exhibit 4.1

AMARIN CORPORATION PLC

AMENDMENT NO. 4 TO

2011 STOCK INCENTIVE PLAN

The Amarin Corporation plc 2011 Stock Incentive Plan (the “Plan”) is hereby amended by the Board of Directors and shareholders of Amarin Corporation plc as follows:

Section 2(v) of the Plan is hereby amended to read as follows:

“ISO Limit” shall mean 31,500,000 Shares, subject to adjustment as provided in the Plan and subject to the provisions of Section 422 or 424 of the Code or any successor provisions.

Section 4(a) of the Plan is hereby amended to increase the total number of Shares available for issuance under the Plan shall be increased by 20,000,000 shares, such that Section 4(a) of the Plan, as so amended, shall read in its entirety as follows:

Section 4. Shares Available for Awards

(a) Shares Available. Subject to adjustment as provided in Section 4(c) of the Plan, the number of Shares in respect of which Awards may be made under this Plan on any day shall not exceed the sum of (i) 31,500,000 Shares, (ii) 3,074,680 Shares (being Shares that remained available for grants under the Company’s existing 2002 Stock Option Plan (the “2002 Plan”) as of July 12, 2011) and (iii) the number of Shares subject to grants under the 2002 Plan that are outstanding as of the Effective Date but subsequently become Lapsed Awards (as defined below) (“the Plan Limit”). Shares to be issued under the Plan may be either authorized but unissued Shares, or Shares acquired in the open market or otherwise. If any award over Shares granted under this Plan or the 2002 Plan expires or is forfeited, surrendered, canceled or otherwise terminated in whole or in part without Shares being issued (“Lapsed Award”), then the Shares subject to such Lapsed Award may, at the discretion of the Committee, be made available for subsequent grants under the Plan; provided, however, that Shares tendered or held back upon exercise of an Option or settlement of an Award to cover the exercise price or tax withholding shall not be considered a Lapsed Award. Notwithstanding the foregoing, the number of Shares available for granting Incentive Stock Options under the Plan shall not exceed the ISO Limit, and Options with respect to no more than 10,000,000 Shares may be granted to any one individual Participant during any one calendar year period.

ADOPTED BY BOARD OF DIRECTORS: March 9, 2015

ADOPTED BY SHAREHOLDERS: July 6, 2015