Improving Access to Homes for Heroes Act of 2021 This bill requires public housing agencies to consider the housing needs of veterans when creating their annual plans and housing strategies, the latter in consultation with agencies that serve veterans. Similarly, the Department of Housing and Urban Development (HUD) must revise its regulations to require jurisdictions that receive funding from HUD to include information relating to veterans in their consolidated plans. HUD must also conduct an assessment of the housing needs of very low-income veteran families and report annually on its activities relating to veterans.