Dvla When I Transfer A Private Plate To A New Vehicle, Does The DVLA Assign A New Plate To The Old Vehicle?

When I transfer a private plate to a new vehicle, does the DVLA assign a new plate to the old vehicle? - dvla

I have a private plate on my Vauxhall and want this for my new Smart transmitted. After the transfer, not the DVLA, I automatically create a new registration number for my old Opel?