Fair Returns for Public Lands Act of 2021 This bill revises the royalty system applicable to leases of public lands for oil and gas production. Specifically, it increases royalty rates, rental rates, and minimum bidding standards for onshore oil and gas leasing. In addition, it establishes a new fee that must be paid by any person who nominates public lands for such leasing. Finally, the bill requires the Department of the Interior to adjust these rates and fees for inflation at least every four years.