Native American Housing Assistance and Self-Determination Reauthorization Act of 2021 This bill provides federal housing assistance to Indians and Native Hawaiians. Specifically, the bill reauthorizes through FY2026 and otherwise revises housing assistance block grants for Indians and Native Hawaiians. Among other things, the Department of Housing and Urban Development (HUD) must award competitive grants to eligible recipients of block grants to carry out affordable housing activities, such as housing rehabilitation projects. The bill authorizes HUD to guarantee housing loans for Indians and Native Hawaiians through FY2026. Additionally, the bill provides statutory authority for the Tribal HUD-VASH program, which provides rental assistance and supportive services to Indians who (1) are veterans of the U.S. Armed Forces, (2) are homeless or at risk of homelessness, and (3) live in or near an area where a tribe or tribally designated housing entity provides assistance for affordable housing. The program must be carried out by HUD in conjunction with the Department of Veterans Affairs. Under the program, grants must be made to entities eligible for housing assistance block grants. HUD may also make renewal grants to entities that have received prior program grants. The bill also requires the Department of Agriculture to set aside and reserve certain rural housing funds for Indian tribes.