If operating on the N-Register you will need to apply for an FCC Aircraft Radio Station Licence which is valid for 10 years, or until the next change of ownership. There are two easy ways to do this:
A) If you are with Southern Aircraft consultancy for your ownership trust, then you can ask them to make an application to the FCC as per their fee schedule here
B) If you are not with Southern Aircraft, you can make an application here through Dockside Radio and they will ensure a quick turnaround. They also offer radio operator permits for those FAA certificated holders who need to have one of these as part of their flight crew documents. See here
Those are the easy ways to deal with the N Reg FCC requirements, and if you have tried to navigate the FCC site you will appreciate what they offer in terms of a quiet life.