Ending Homelessness Act of 2021 This bill expands the housing choice voucher program and provides assistance to homeless individuals and families. Specifically, the bill provides FY2022-2025 funding for the expansion of the housing choice voucher program for certain extremely low income families. Furthermore, beginning in FY2026, the bill creates and funds an entitlement to housing choice vouchers for certain extremely low income families. Eligibility for the entitlement expands annually, extending to low-income families by FY2030. The bill also reduces the geographic area used to calculate an area's fair market rent for purposes of voucher payment standards and prohibits the use of criminal history in determining eligibility for certain housing assistance. Additionally, the bill prohibits housing discrimination on the basis of a renter's source of income or a renter's veteran status. The bill also provides additional FY2022-FY2026 funding for the Department of Housing and Urban Development (HUD) to assist the homeless, including to award emergency relief grants in jurisdictions with the highest need and award grants to provide outreach and coordinate services. Furthermore, the bill provides additional FY2022-FY2026 funding for the Housing Trust Fund, which provides affordable housing for extremely low-income and very low-income families. While this additional funding is available, HUD must ensure that priority for occupancy in assisted units is given to individuals and families who are homeless. Finally, the bill permanently reauthorizes certain homeless assistance grants and makes permanent the U.S. Interagency Council on Homelessness.