Further Surface Transportation Extension Act of 2021 This bill extends and revises provisions related to federal-aid highway, transit, highway safety, rail, and other surface transportation programs of the Department of Transportation. Specifically, the bill extends FY2021 enacted levels of funding through December 3, 2021, for federal-aid highway, transit, and safety programs; and extends expenditure authority through December 4, 2021, for the Highway Trust Fund, Sport Fish Restoration and Boating Trust Fund, and the Leaking Underground Storage Tank Trust Fund.