Veterans Employment Training Act or the VET Act This bill requires the Department of Labor to award grants to employers to enter into partnerships with community colleges to create programs for training veterans for new jobs with such employers. A "new job" is defined as a job that: may include a new position within an existing job category that is not a job of a recalled worker, a replacement job, or any other job that existed in the employer's business within the one-year period preceding the date of hire; is not a job that existed in a business operation or substantially similar business operation of the employer formerly located in another location that was closed or substantially reduced by the employer; and results in a net increase in employment for the employer.