Safe Schools Improvement Act of 2021 This bill requires states to direct their local educational agencies (LEAs) to establish policies that prevent and prohibit bullying and harassment of elementary and secondary school students. In particular, these policies must prohibit bullying and harassment based on race, color, national origin, sex, sexual orientation, gender identity, disability, or religion. Further, LEAs must provide (1) students, parents, and educational professionals with annual notice of the conduct prohibited in their disciplinary policies; (2) students and parents with grievance procedures that target such conduct; and (3) the public with annual data on the incidence and frequency of that conduct at the school and LEA level. The Department of Education must conduct and report on an independent biennial evaluation of programs and policies to combat bullying and harassment in elementary and secondary schools. The National Center for Education Statistics must collect state data to determine the incidence and frequency of the conduct prohibited by LEA disciplinary policies.