Navy SEAL Chief Petty Officer William “Bill” Mulder (Ret.) Transition Improvement Act of 2019 This bill requires the Department of Labor and the Department of Veterans Affairs (VA) to make improvements to the Transition Assistance Program (TAP) that serves members of the Armed Forces who separate, retire, or are discharged from service. Among other requirements, the bill extends by five years the pilot program for providing off-base transition training for veterans and their spouses. Labor must select no fewer than 50 locations to implement the training, and at least 20 shall be states with a high rate of veteran unemployment. The bill requires the VA to make grants to eligible organizations for the provision of transition assistance. Additionally, the bill requires the VA to enter an agreement with an independent entity with experience in adult education to report on the efficacy of TAP. The VA must also conduct a five-year longitudinal study of TAP on three separate cohorts who have separated from the Armed Forces. Finally, the bill grants access to the VA and Labor to certain information reported by employers to states' new hire directories in order to track employment of veterans.