can I do that, or do I have to renew it first?

You might want to check with the DMV concerning this, as each state may have their own laws regarding this. I see by your profile you live in CA, and if I remember in CA the plates are transferred with the vehicle? In NY you can sell a vehicle where the registration has lapsed, as the new owner will either transfer their own plates, or obtain new ones when they go to the DMV to register it.

I was in Texas where the plates move with the car. The registeration was not expired yet (expired that month though). When the new owner went to the DMV for the title work, new registeration was included into the cost. As said before, it varies from state to state but, the DMV will usually handle it.

Edit: best thing is to go to the DMV with the new owner when you sell the car. That way if anything was done wrong, you can fix it right then.