Post-9/11 Veterans' Mental Health Care Improvement Act of 2021 This bill addresses mental health care provided by the Department of Veterans Affairs (VA), including by requiring the VA to expand access to mental health care, expand its mental health workforce, and conduct studies and research. Among other requirements, the VA must increase the number of full-time equivalent employees at Vet Centers, expand specified scholarships and loan repayment programs for mental health providers and students, offer mental health consultations to certain veterans, improve the assessment and treatment of veterans with sleep disorders, and perform various studies and research related to mental health issues and care.