Improving Housing Outcomes for Veterans Act of 2021 This bill requires the Veterans Health Administration (VHA) to provide medical center staff and homelessness service providers of the Department of Veterans Affairs (VA) with information related to best practices for the collaboration on activities under the Department of Housing and Urban Development's Coordinated Entry program. The VA must also ensure that the information and related resources are accessible to VA medical center staff and homelessness service providers. Additionally, the bill requires the VHA to communicate with VA employees who have responsibilities related to homelessness assistance programs regarding (1) the measurement of performance by the VA's Homeless Program Office, and (2) how to obtain and provide feedback about the performance measures.