Veterans Census-Enabled National Treatment Equitable Resource Supplement for Mental Health Act of 2021 or the Vet CENTERS for Mental Health Act of 2021 This bill requires the Department of Veterans Affairs (VA) to ensure the number of Vet Centers in certain states is increased by not less than one additional center if the VA determines the state meets specified requirements. The VA must also establish a community-based outpatient clinic in each state that does not share a land border with another state, is located not less than 2,000 miles from the contiguous United States, and contains no such clinic.