Native Educator Support and Training Act or the NEST Act This bill establishes scholarships, loan forgiveness plans, and training programs for students and educators who commit to teaching in Bureau of Indian Education (BIE) schools or other specified schools serving Indian students. The bill establishes three scholarship programs: (1) the Indian Student Educator Scholarship Program for students seeking degrees, (2) the Indian Educator Scholarship Program for Indian students seeking degrees, and (3) the Indian Educator Graduate Fellowship Program for Indian students seeking graduate degrees. Recipients of the scholarships must commit to working for a BIE school, a tribal early childhood education program, or other specified schools or agencies for the greater of three years or the number of school years that the scholarship funded. The bill also establishes loan forgiveness programs for educators and Indians who have taught for at least five consecutive years at BIE schools or local educational agencies with high percentages of Indian students. The bill extends the federal Perkins Loan Cancellation Program to educators teaching in BIE schools or in Native American language immersion programs. The bill authorizes professional development grants for Native-serving elementary and secondary schools. It also establishes the Native American Language Teacher Training Program to provide grants for institutions of higher education to develop training programs for Native American immersion and language teachers.