New Jobs Training Act This bill requires the Department of Labor to award grants to employers to partner with community colleges to create programs for training individuals 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 in the year 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.