@cal6308 If the 'new' phone takes the same size sim (these days it's usually a nano-sim), then it is fine.
Basically, if you can fit it into the phone, then it's fine.
The only problem that people sometimes find is that a phone won't work as it is locked to a network other than Three - this is not so common these days as they almost all come unlocked, but can happen if the phone is a few years old.
