Kinda confused... how do you sign a contract with a new team if you are still part of another team (i.e., if the trade hasn't happened yet)? Do they mean agree to a new contract?
They probably mean agree to a contract. Most of the time when a team is trading to get a player, they get permission to start contract talks to make sure that they can agree on a contract. This helps the team getting the player save $$ since players being traded usually have a huge salary at the end of their contract.
So if Peppers has 4 teams, I'm curious if the NFL has even 2 teams that would pay him QB money for just-a-guy production?