If it's a 'pushed out' nano SIM (from the existing one), it should work in exactly the same way as the old one.
A new nano SIM, that's been specifically ordered to replace the old one, should have the same phone number and therefore the same amount of credit (which is stored on GiffGaff's servers, not on any phone or SIM). However the contacts won't be transferred across.
It's possible to copy the data to a PC and then transfer it to a new card. However that would involve purchasing an adapter so that the PC can read/write data to the cards. An independent mobile phone shop, or market stall, can also be the job but, again, that would cost money. Unless your father has got thousands of contacts, it would be simplest to write down the information from the old card and then manually enter it into the new one. (That's what I'd do anyway!)