You do not need any special state-level permits or licenses; you only need to follow the federal ATF process.
It is legal to hunt with a suppressor in PA for big game (deer, bear), predators (coyotes, foxes), and varmints. The Pennsylvania Game Commission approved suppressor use for hunting in 2016.
In Pennsylvania, suppressors are classified as "offensive weapons," but their possession is fully legal if they are properly registered with the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF).
The process has shifted from months of waiting to a more streamlined digital system. Most buyers use specialized services like Silencer Shop or Silencer Central to manage paperwork. Pennsylvania – Silencer Central