Can an expungement help me when applying for a gun permit?

Yes.  the official New Jersey Firearms Identification Card Application Form relating to past criminal convictions or arrests specifically exclude records that have been expunged or sealed. Your New Jersey expungement will also remove any federal firearms disability that arose on account of the New Jersey conviction. This follows from Title 18, Section 921(a)(20) of the United States Code. That provision states: "Any conviction which has been expunged...shall not be considered a conviction for purposes of this chapter, unless such...expungement...expressly provides that the person may not ship, transport, possess, or receive firearms." Note, however, that if you previously had a gun permit that was revoked, or if you previously applied for and were denied a gun permit, you would have to divulge that fact and explain the reasons even though those reasons related to matters that were later expunged.