Native American Child Protection Act of 2021 This bill reauthorizes through FY2027 and otherwise revises certain programs related to the prevention, investigation, treatment, and prosecution of family violence, child abuse, and child neglect involving Indian children and families. Specifically, the bill revises the Indian Child Abuse Treatment Grant Program to encourage the use of grants for culturally appropriate treatment services and programs. The bill renames the Indian Child Resource and Family Services Centers as the National Indian Child Resource and Family Services Center. It also requires the center to (1) provide advice, technical assistance, and training to urban Indian organizations; (2) develop technical assistance for Indian tribes, tribal organizations, and urban Indian organizations; and (3) develop model intergovernmental agreements between tribes and states to prevent, investigate, treat, and prosecute incidents of family violence, child abuse, and child neglect involving Indian children and families. Additionally, the bill revises the Indian Child Protection and Family Violence Prevention Program to allow Indian tribes, tribal organizations, and intertribal consortia to use program funds for additional activities, such as operational costs for child protective services.