You cannot possess a handgun outside of the home in New Jersey unless you have a permit to carry or properly transporting the gun to or from a gun range, gun smith, or from the place of purchase to your home. A NY handgun or license has no impact whatsoever in this equation in terms over avoiding a charge for unlawful possession of a handgun. There is no reciprocity in NJ for your NY firearm rights.
Home Is There Reciprocity For a NY Handgun License in New Jersey?