Strengthening Career and Technical Education for the 21st Century Act This bill reauthorizes through FY2023 and increases funding levels for Department of Education (ED) grants to states, national programs, and tribally controlled postsecondary career and technical education (CTE) institutions under the Carl D. Perkins Career and Technical Education Act of 2006 to support CTE programs for secondary and postsecondary students. It repeals the authorization for certain occupational and information activities and the separate mandate for tech prep education. Beginning in FY2021, states must receive at least 90% of their previous year's allocation of basic state CTE grants. The bill permits states to: reserve up to 15% (currently 10%) of their grant funds for innovative CTE activities in rural areas or areas with higher numbers of CTE students, and set their own annual targets on the core indicators of performance at both the secondary and postsecondary education levels without ED's approval. The bill modifies grant application processes for states and localities and performance measures for evaluating CTE programs. It prohibits ED from withholding funds from states that do not meet certain performance measures. The bill amends the Wagner-Peyser Act to expand the duties of state agencies with respect to providing workforce and labor market information.