If you enter California after being discharged, you do not have to register your passenger vehicle or trailer coach right away as long as it has valid out-of-state plates and registration. You have 20 days from the date you take steps to become a California resident to register it and avoid penalties.
There is nothing to apply for. Register the vehicle at a Department of Motor Vehicles office within 20 days of the date you take steps to become a California resident.
Your out-of-state registration and plates, and your discharge paperwork.