Clean Energy Jobs Act of 2019 This bill directs the Department of Energy (DOE) to establish and carry out a comprehensive nationwide program to improve education and training for jobs in energy-related industries with existing or expected worker shortages. Emphasis shall be placed on increasing the number of skilled individuals from underrepresented groups trained to work in those jobs. DOE must establish an online resource center to maintain and update information and resources on training programs for such jobs; and as a resource for specified agencies, organizations, and apprenticeship programs working to develop and implement training programs for the jobs. The Department of Labor must provide grants to certain businesses or labor management organizations to pay the wages of employees when they are receiving training for jobs in the renewable energy, energy efficiency, grid modernization sectors or for reducing greenhouse gas emissions.