Once you have requested Admission to the Old Camp by talking to Diego, Thorus, Diego again, and then Thorus again, ask Thorus if he has a task for you and convince him you're skilled enough. His task is for you to get rid of a guy called Mordrag, an unwanted visitor from the New Camp. Go and see Mordrag (he's near the south gate). If you only care about keeping Thorus happy, kill Mordrag. This will be no easy task at this point, however.
If you want easy access to the New Camp or are simply unable to beat Mordrag, tell him "you have a problem" and he'll get ready to leave. He will lead you directly to the New Camp. When you get there he will give you his ring as a sign that you are a friend. You can later use this as a bargaining tool for joining the New Camp.
While at the New Camp feel free to talk to people, do quests, or steal things; when you're ready head back to the Old Camp and tell Thorus the good news. If you didn't kill Mordrag he'll say he'd have preferred if you had, but either way he's satisfied and promises you his vote.