Youth Workforce Readiness Act of 2019 This bill requires the Department of Labor to award grants to certain national youth-serving organizations for comprehensive workforce readiness programs provided to youth that take place before or after school, during summer vacation or holiday, or on the weekend (i.e., out-of-school-time programs). Such grants must be used to develop and implement youth workforce readiness programs, including for activities such as on-the-job and leadership opportunities, internships, and other supportive services. The bill also requires local workforce development boards to establish youth councils as subgroups of the boards.