Private Plates

[Jobt]

Hi all - I am in the process of removing my private plate as I'm selling my car. I have received my new tax disc etc from the DVLA but I was just wondering how long I have to change the number plates on the car? Am I still able to drive it with the old plate/tax disc on display until I can get to a garage to get some new plates made up?
Any advice would be much appreciated!