Human Trafficking and Exploitation Prevention Training Act of 2021 This bill establishes demonstration grants to train students, teachers, and school and youth development personnel how to better understand, recognize, prevent, and respond to human trafficking and the exploitation of children and youth. Eligible grantees include tribal nations and organizations, nonprofits, state agencies, and elementary and secondary schools. The Office on Trafficking in Persons within the Administration for Children and Families must award the grants.