You do not get a "license" for a suppressor. You find a dealer who handles Title 2 weapons and buy it from him.
You have to pay a $200 tax and submit a form to the ATF for approval. Usually, the dealer will assist you with that part of it.
Your CCL is issued by your state, and this is a federal thing. The two are actually unrelated.
In the depth of winter I finally learned that there was in me an invincible summer.