While you can register your car in a different state than your driver’s license, most states require you to update your driver’s license within 30 days of moving to the state. To avoid any penalties or fines, you’ll likely need to update your driver’s license as well.
There are a handful of states that allow you to register your car in a different state than your license, so long as you can prove residency within that state. However, Missouri is not one of those states.