When you purchase your leased vehicle, you change the ownership of the vehicle. The lessor owns a leased vehicle with the lessee listed on the registration. Following a lease buyout, you must re-register and re-title the vehicle in your name. When you do this, the registration on your leased vehicle ends, and you begin a new registration term; the time remaining on the leased vehicle’s registration does not transfer to the new vehicle.
If you renew the registration on a leased vehicle immediately before you buy out your lease, that registration time will not transfer to the new vehicle.
When you purchase a leased vehicle, the lessor should provide you with the title of the vehicle signed over to you. Bring that title and bill of sale to any DMV office to re-register and retitle the vehicle in your name.
You will be responsible for a new registration fee, title fee, and 6% purchase and use tax on the vehicle's residual value. You may keep your existing plates, but the time on those plates will start over when you re-register the vehicle.