Youth Corps Act of 2021 This bill authorizes the Department of Labor to make grants to public or private nonprofit agencies or organizations to carry out Youth Corps programs that utilize the Youth Corps model to provide low-income youth (age 16 and not more than age 24) with education and work readiness training. The term Youth Corps model means a youth education and training program for which an eligible entity provides eligible youth with stipended or paid work experience and basic and technical skills training leading to (1) enrollment in postsecondary education or training, (2) attainment of an industry-recognized certification or credential, (3) meaningful employment in the economy of the 21st century, or (4) military service.