Preparing and Retaining Education Professionals Act of 2021 or the PREP Act of 2021 This bill reauthorizes and revises certain grant programs to address shortages of teachers and school leaders (e.g., principals) in elementary and secondary schools, including shortages in rural areas and related to specific positions (e.g., special education and English language instruction). First, the bill makes permanent and otherwise revises the Teacher Quality Partnership program (which provides grants to improve the quality of teachers and enhance professional development activities). In particular, the bill revises the program to (1) expand the purpose of grants to include the recruitment of well-prepared individuals, including individuals from underrepresented populations, into the teacher and school leadership force; (2) include training and professional development opportunities for school leaders; and (3) establish a grant program to address workforce shortages or increase workforce diversity. Next, the bill makes permanent and otherwise revises the Augustus F. Hawkins Centers of Excellence program (which provides grants to establish teacher preparation programs at minority-serving institutions). Further, the bill allows grants to be used for school leader preparation programs. Additionally, the bill aligns activities within teacher preparation programs at predominantly Black institutions, Native American-serving institutions, and other minority-serving institutions with certain changes made to the Teacher Quality Partnership program. The bill permanently reauthorizes the Minority Science and Engineering Improvement program (which provides grants to improve science and engineering education at predominantly minority institutions).