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