Per the New York City Department of Environmental Protection:

Any person already certified by the NYC DEP to engage in ASBESTOS HANDLING (certified asbestos handlers, restricted handlers, handler-supervisors, and investigators) whose certification hard card expired on March 15, 2020, or later, may continue to work using their existing cards until August 31, 2020.

No further documentation is necessary to work with an expired card.

For more information, visit:
https://www1.nyc.gov/site/dep/environment/asbestos-handler-certification-applications.page