In reply to TheDrunkenBakers:
If I understand correctly, it’s her iphone already and all you are doing is putting a new sim in it for the new contract?
Normally just remove old sim and insert the new one. I’ve done this a few times with no problems. Make sure that she has accessed her voicemails prior to the change/old sim disconnected as that maybe lost even with the same network provider.
If the old sim was only used on an iPhone, the SIM card will not normally* have anything added to it as Apple don’t allow that. You can take off (import) contacts from a SIM card previously used in another phone though if the old sim ever had contacts added previous to the iphone use.
* assumes it was never jailbroken.
As others have said cut up the old SIM card after it’s disconnected from the network.
BTW If you are unsure if there are contacts on the old sim and want to be safe use the iPhone import sim contacts under settings/contacts before removing the sim (make sure that the iphone has been backed up previously just in case something goes wrong).