Tribal HUD-VASH Act of 2023 This bill provides statutory authority for the Tribal HUD-VASH program, which provides rental assistance and supportive services to Indian veterans who are homeless or at risk of homelessness and living in or near an area where a tribe or tribally designated housing entity provides assistance for affordable housing. The Department of Housing and Urban Development (HUD) may use up to 5% of rental assistance amounts under the HUD-VASH program, which provides housing assistance to homeless veterans, for the Tribal HUD-VASH program. The Tribal HUD-VASH 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 make renewal grants to entities that have received prior program grants.