Here is your chance.  Email them at Pawnstarstvshow@gmail.com
You can find out more at this link:
http://tinyurl.com/6lkngsq

Of course, if you just want to visit the shop or sell an item without being on TV you can do that any day.  Gold And Silver Pawn is at 713 S Las Vegas Blvd between the Strip and Downtown.   Half of the store is Pawn Stars merchandise, but if you like the show you will probably like the store.