Grant Residency for Additional Doctors Act of 2021 or the GRAD Act of 2021 This bill requires the Department of State to take certain actions to expedite the processing of visas for aliens entering the United States for graduate medical education or training. Specifically, the State Department shall designate an officer or employee whose sole responsibility from March through June (and in any other time period as necessary) is to facilitate the expedited review of visa applications for such aliens. The State Department shall also provide relevant Foreign Service officers with training related to medical graduates and medical graduate programs in the countries where the officers are serving.