According to the New Jersey Motor Vehicle Commission, if you have recently moved to New Jersey, you are required to transfer your out-of-state license within 60 days of permanent New Jersey residency or before your current license expires. Your license cannot be transferred to a New Jersey license if you are under 18 years old. Instead, you must complete the Graduated Driver License (GDL) program requirements.
There are 3 options to complete the program - The Early Bird (for 16 years old), The Young Adult Road (for those 17 to 21 years of age) and the Adult Road (for those 21 or older). As a 16 1/2 year old you would take the Early Bird route.
With this choice you first must receive a Student learner's permit (minimum six months of supervised driving) then progress up to a provisional license (minimum one year of restricted but unsupervised driving) and finally graduate to the basic driver license (must be 18 years old).
To find out if you can drive in New Jersey with your NYS license until you turn it in and start the NJ graduated licensing program, check with the NJ MVC.