Rural Educator Support and Training Act or the REST Act This bill establishes several new grant programs for students who are training at institutions of higher education to become educators in rural schools and provides additional federal student loan forgiveness for rural educators. Specifically, the Department of Education (ED) must award undergraduate scholarships and graduate fellowships to students who are studying to become educators in rural schools and who agree to serve such schools for three or more years. ED may also award grants to eligible educational agencies for the purpose of (1) reimbursing eligible rural educators for out-of-pocket costs associated with obtaining national board certification, and (2) increasing annual compensation for eligible rural educators who have become certified. In addition, a teacher who is employed for five consecutive years in a rural school shall be eligible for up to $17,500 in federal student loan forgiveness.