VA Governors Challenge Expansion Act of 2021 This bill provides statutory authority for the Governors Challenge Program and otherwise revises the program. The program assists states and local communities with developing and implementing veteran suicide prevention activities. In particular, the bill expands the program by directing the Department of Veterans Affairs (VA) to make grants to states and American Indian and Alaska Native tribes for developing and implementing plans to prevent veteran suicides. Further, the bill requires the VA to provide technical assistance to tribes.