ExxonMobil needs to enhance its long-term value by revamping the board, imposing capital discipline, investing in more sustainable energy and overhauling management compensation, according to a new investment firm.

San Francisco-based Engine No. 1, which said it seeks to build long-term value through “active ownership,” on Monday said it would nominate four independent candidates to the board at the 2021 annual meeting to advance its plan.

The letter to the board outlines proposed changes to “evolve with changing industry dynamics.” Besides adding independent directors, Engine No. 1 principals want ExxonMobil to use “more stringent approval criteria for new capital expenditures, including lower required break-even oil and gas prices.” In addition, they called for...