Public Diplomacy Modernization Act of 2021 This bill establishes measures related to public diplomacy conducted by the Department of State. Specifically, the bill directs the State Department to appoint a Director of Research and Evaluation in the State Department's Office of Policy, Planning, and Resources for Public Diplomacy and Public Affairs. The director's responsibilities shall include (1) overseeing research to improve State Department public diplomacy strategy and tactics, and (2) developing guidance and training for public diplomacy officers on interpreting and implementing public diplomacy-related research. The bill permanently reauthorizes the U.S. Advisory Commission on Public Diplomacy and directs the commission to establish the Subcommittee for Research and Evaluation. The subcommittee shall provide advice regarding audience research, digital analytics, and impact evaluation for State Department activities. The bill directs the State Department to establish a working group to analyze a potential transition to a shared-services model for human resources, travel, purchasing, and all other executive support functions for all bureaus that report to the Under Secretary for Public Diplomacy. The State Department shall adopt certain guidelines related to collecting and utilizing information in the event of a closure or consolidation of a public diplomacy facility.