Native Educator Support and Training Act or the NEST Act This bill amends the Higher Education Act of 1965 to establish scholarships, loan forgiveness plans, and training programs for educators who commit to teaching in Native American or Bureau of Indian Education (BIE) schools. This bill establishes three scholarship programs for students who are seeking degrees in education or school administration at institutions of higher education and commit to teaching in Native American or BIE schools: the Indian Student Educator Scholarship Program for students seeking degrees, the Indian Educator Scholarship Program for Indian students seeking degrees, and 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 school serving Native Americans, or other specified schools and agencies for the greater of three years or the number of school years that the scholarship funded. The bill establishes loan forgiveness programs for educators and Native Americans who have taught for at least five consecutive years at BIE schools or local educational agencies with high percentages of Native American 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.