Helping Unleash Benefits and Services for Veterans Act of 2021 or the HUBS for Veterans Act of 2021 This bill establishes a grant program to assist the transition of military personnel to civilian life. It directs the Department of Labor to carry out a five-year program of grants to nonprofit organizations that assist the transition of the following persons from Armed Forces service to civilian life: members eligible for preseparation counseling, former members who are transitioning to civilian life, and spouses of such members or former members. Funds must be used for a broad range of supportive programs, such as job recruitment training.