If the phone is under contract with a different company, then the phone is probably also locked. To get it unlocked you would have to contact the prior company (Verizon) and have them unlock it. However, if you owe them for the phone or other things, they may well not unlock it for you. They are not required to do it if you don't own the phone. Now if you own the phone (no payments due on the phone) but owe them for something else, then they should not be able to tell you they won't unlock it. I mean they can try, but in such a case I would speak to someone higher than the standard CSR (Customer Service Representative). They have to unlock the phone if it is fully paid for.
Now in regard to using the phone on a different carrier, once...