If you have a parking e-permit (bought via RingGo) and you want to use it with a new vehicle that you intend to keep, you need to cancel your permit and buy a new one for the new vehicle.
If a refund is due on the cancelled permit then it will be applied to the card used for the original payment.
You'll be able to use your new permit straight away.
There is a different process for using a parking permit with a courtesy car.