Teachers and School Leaders need Education And Development to be Empowered Resources in Schools Act of 2021 or the Teachers and School LEADERS Act of 2021 This bill reauthorizes through FY2027 and otherwise revises the Teacher Quality Partnership program. This grant program provides training and professional development opportunities for prospective and new teachers through partnerships between (1) high-need school districts, schools, or early childhood education programs; and (2) institutions of higher education. Specifically, the bill expands the program to include training and professional development opportunities for principals and other school leaders. In addition, the bill expands the types of entities that qualify as partners to high-need schools or programs to include entities that are educational organizations, entities operating programs that provide alternative routes to state certification of teachers or school leaders, or educational service agencies.