Two factors to consider are:

1. is it your oldest line of credit? If it’s your oldest account and others are a lot newer, short account age is a listed factor on at least a couple of the main scorers.

2. will closing it take you over 30% credit utilisation? Ideally maintain a healthy credit limit that means you keep below using 30% of it at any one time. If you close the card and lose that limit, what do you have left?

Of course you will also get a hit from any credit application you make for your own new card.

However if you don’t need to make significant other applications anytime soon, get a new card first if your credit is good, then close the old one. Numbers will drop for a bit but climb back up soon enough.

There could be other factors too but those are the ones that come to mind