Sly's friend Nek has gone missing. Head over to the wall near the arena and talk to Fletcher. He tells you more about Nek, and asks you to go find him. If you've collected ingredients for Snaf's Recipe you already know what happened to him; if not, go do it, as it's a great way to solve two quests at the same time. You can find Snaf along the lower path left of the north gate.
Once you have found the amulet tell Fletcher what happened, then return to Sly. He doesn't really care that Nek is dead, what he really wants is the amulet. If you're not yet sure you want to join the Old Camp you can just hold onto it for now by simply not reporting back to him yet. All he'll give you is some experience and his promise to speak up for you in front of Diego, but he won't do this until you give him the amulet.