If you have a private number plate, you’ll be able to keep it by arranging to transfer the registration through the DVLA at a fee of £80. Once transferred, you will receive a new V5C document from the DVLA which you must bring to the handover.
It’s okay if you haven’t got a car to put the plate on straight away – the DVLA provides a Retention Scheme where a registration is placed on to a certificate of entitlement until the owner is ready to transfer the plate to a new car at their own convenience