Just changed cars and the newer car has a 13 pin tow-bar electrics. I've looked around and this seems to be typical for more modern cars - I'm guessing this is retro fit as the car isn't very modern, it's 15 years old (Merc 4x4)!
Anyway, I've got 7 pin electrics on my trailer and on my Thule carrier.
It it simply a case of using one of the zillions of 7-to-13 pin adapters on various auction and selling sites, or am I better steering clear of adapters and getting new electrics fitted?
13 pin is so much better, I'd recommend rewiring unless you have a good reason not to (e.g. likely to use other old vehicles).
I did my bike carrier and folding camper. If you're halfway competent with wire stripping and terminals, with a bit of patience and care it's easy to do yourself — particularly if you only have the black 7-pin (12N) plug and not the supplementary grey one (12S), as you'll have fewer wires to connect.
I bought two 13-pin plugs, one green cover and some self-amalgamating tape to waterproof it all. For the camper, I bought a few metres of decent 12-core cable from a local caravan shop to replace the twin 7-core but you may not need that if you have a single cable with enough slack.
Personally I just use an adapter when towing my trailer or using my bike carrier and I've never had a problem. You would need a 13 pin to 7 pin adapter (not 7 pin to 13 pin). Just be aware that the 13 pin connection twists into place to secure the connection.
I used to use a 13 pin to twin 7 pin adapter with the trailing cables but to save them dragging on the ground I changed to the adapter shown in the link below. If you only need the Black socket for the trailer lights then just lift up the black flap and push in the 7 pin Black plug. The Grey socket can remain absent of a plug without any issues.