Tribal Economic Development Act of 2021 This bill amends provisions relating to tribal economic development (TED) bonds issued to promote community development projects in Alaskan Indian tribal areas. Specifically, the bill increases the national tribal economic development bond limitation to $4 billion. It also eliminates the requirement that TED bond proceeds be used solely on Indian reservations and permits bond proceeds to be used for economic development by any qualified Native user which includes any tribal entity, Alaska Native Corporation, and entity that is majority-owned and controlled by an Indian tribe or Alaska Native Corporation. The bill also allows third parties to guarantee the repayment of TED bonds.