Old iPhone with old sim card?

Mum just got a new iPhone, so gave her old one to my sister.
My sister did not have an appropriate sized sim card, so they guy at the store cut it down.
Mum's new sim card is working, but when we put my sisters in the old phone, it just keeps saying no service.
What do we do?
Can we use it or not?

It may have been cut badly for some reason. I'd take it back to the store and ask for a new sim card with the same number.

Either it was cut bad or the phone is locked to a different carrier.