21st Century Energy Workforce Act This bill directs the Department of Energy (DOE) to establish a National Center for Excellence for the 21st Century Workforce Advisory Board to foster strategic vision, guidance, and networks for the energy industry. The purpose of the board is to (1) support and develop training and science education programs, (2) align apprenticeship programs and industry certifications to further develop succession planning in the energy sector, (3) integrate educational standards to develop foundational skills for elementary and secondary education and postsecondary education to create a pipeline between education and career, and (4) support the replication of existing model energy curricula. DOE shall also establish a pilot program to award grants to eligible entities for job training programs that lead to an industry-recognized credential.