Supporting the Teaching Profession through Revitalizing Investments in Valuable Educators Act or the STRIVE Act This bill amends the Higher Education Act of 1965 to provide qualifying teachers with a new, incremental loan-cancellation program. Specifically, with respect to a 12-month period, the Department of Education (ED) must cancel a specified portion of a borrower's qualifying Federal Direct Loan Program loans if the borrower: (1) has made 12 consecutive on-time monthly payments, (2) is employed in a qualifying teaching position at the time of such cancellation, and (3) was employed in a qualifying teaching position during the period in which the borrower made the 12 payments. After a borrower has received such partial loan cancellation for a specified number of years, ED must cancel the borrower's eligible loans in full. The bill also: increases and extends funding for teacher training; makes changes to the Teacher Education Assistance for College and Higher Education grant program, including by increasing annual award amounts and making early childhood teachers eligible for such grants; requires ED to award grants to states to subsidize teacher certification and licensing fees for low-income individuals who have entered the teaching profession; expands the teacher quality partnership grant program to include early childhood educators; and increases the tax deduction for school expenses and extends the deduction to early childhood educators.