Trevor is now an officer. Officer's do not have contracts like enlisted do. They may incur obligations for accepting a promotion, a change in permanent station, or tuition assistance while pursuing a master's degree, but it's not called a contract.
Trevor tells the front desk he is checking out, then after a conversation with Roxy, he says he's going to pack. He would have needed to pack before checking out, as you can't get back into the room after checking out.