Here is the helpful link from Indeed.com Guide to Earning Aircraft Dispatcher License
To eliminate any doubt as to whether or not these requirements have been met, you should check with your local FAA FSDO office. Note: ATP applicants are no longer required to present their qualifications to an FAA Inspector prior to the test for an FAA authorization. A current First-Class Medical Certificate is no longer required to sit for the exam. Only a 3rd Class is required for the check ride in an airplane. A medical is not required if taking the ride in the simulator.