If you plan to become a New Jersey resident, you have 60 days to apply for your New Jersey State license. If you do not plan to become a resident, then you are fine to drive with your out-of-state license as long as it is not suspended, revoked or expired.
If you possess a valid NJ Driver's license from another state, you do not need to take the NJ Driving Exam. You have 60 days to replace your out-of-state license with a New Jersey State Driver's License. To do this you will need to visit a local MVC office with legal documents that pass the 6 point identity and address verification. For more information about acceptable documents visit this website: https://www.nj.gov/mvc/Licenses/DocumentSelector/index.htm.