Wildlife Veterinarians Employment and Training Act or the Wildlife VET Act This bill provides grants for veterinarian positions at wildlife or veterinary institutions and provides incentives for students to enroll in wildlife or zoological veterinary medicine programs. Specifically, this bill authorizes the Department of the Interior to award grants to wildlife or veterinary institutions to create additional clinical and research positions for such veterinarians. Interior must establish a program that pays the student loans of graduates and students of institutions that provide doctoral degrees in veterinary medicine or graduate degrees in veterinary medicine. Interior must also establish a program that awards scholarships to students enrolled in an accredited school or college of veterinary medicine. In exchange for the loan payment or scholarship, students must agree to serve for at least four consecutive years at a wildlife or veterinary institution as a wildlife or zoological veterinarian. In addition, Interior must also (1) establish a pilot program to award grants to accredited schools and colleges of veterinary medicine to develop or improve new or existing curricula that specialize in wildlife or zoological veterinary medicine, and (2) award grants to eligible wildlife or veterinary institutions to establish or expand training programs that will enhance the ability of a trainee to practice as a wildlife or zoological veterinarian.