By successfully petitioning the court to expunge your criminal history, you could be eligible to lawfully possess a firearm in New Jersey again. However, in order to do so, you must first go through the traditional process and make an application for a Firearms Purchasers Identification Card (FPIC). This application should be submitted through the Chief of Police of the town that you reside in.
By having your criminal case history expunged, you can answer certain questions on the application more favorably. This could certainly increase your chances of obtaining your FPIC and, eventually, a firearm. However, there are circumstances under which you may still be denied a gun permit in Monmouth County.