Partnering Aspiring Teachers with High-need Schools to Tutor Act of 2021 or the PATHS to Tutor Act of 2021 This bill expands access to tutoring in hard-to-staff and high-need schools by establishing a grant program and providing certain incentives to teachers. Specifically, the bill directs the Department of Education (ED) to award competitive grants to local consortia to carry out tutoring programs. Local consortia refers to partnerships between teacher preparation programs, local educational agencies or individual schools, and community-based organizations. Grant recipients may use these funds for certain activities, including matching and placing tutors, purchasing instructional materials and connectivity resources, and providing transportation and meals to students who attend the tutoring program. Further, ED must enter into an interagency agreement with the Corporation for National and Community Service to include tutor positions as approved national service positions. Finally, the bill allows tutoring to count toward service requirements for the Teacher Education Assistance for College and Higher Education grant program.