State statutes or laws will dictate if you need to have a driver's license in the same state in which your car is registered and insured. Some states require you to insure and register your vehicle within a certain time period of becoming a resident of that state but do not mention the need for you to turn in your out of state license and obtaining a new state driver's license.
Other states, such as California, require that once you become a resident of the state you must get a state driver's license and also register and insure you car in the state within a certain period of time. New Jersey is the same way, requiring you to surrender your out-of-state license and change over the title and registration on your vehicle once becoming a resident of NJ.
To find out what the state you are residing in requires, contact your local department of motor vehicles.