Your first move is to call the court clerk, and ask the clerk if they will accept payment, and if a failure to appear charge has been added. In some places they will let you pay the original fine, or add a warrant fee. Other places will add the new failure to appear charge along with issuing a warrant.
In either case, you are probably best served by having a local attorney handle the matter for you, to avoid it showing up on your driving record, where your insurance company is able to see it. Most traffics tickets can be amended to a non-moving violaton for a nominal fee and a slightly higher fine with court costs.
If you have further questions, feel free to contact me through the contact information on my website. This is a general description of legal rules practices, and is not intended to be relied upon as legal counsel in this particular situation. There is no attorney-client relationship established by the answering of this question, and no expectation of representation in offering this general information.
Contact the municipal court and explain the situation to them. They will advise you what options you have in that court. Each of the courts are run slightly differently, so you cannot assume that an experience that you may have had in another court will be handled the same way in this one. Call them.
The warrant may indicate that your NJ driving privilege is already suspended. The best you can do is post bail to vacate the warrant and the matter will be listed for a new court date. You or your attorney must appear in court on the new court date to resolve the matter. Someone else may post bail for you.
Answers to questions are for general purposes only and do not establish an attorney-client relationship.
Depending on where out of state you are and why, you may be able to hire local counsel to appear on your behalf to handle the entire issue without your having to appear. The only way to know for sure is to speak with local attorneys and to provide the documentation to them so that they can contact the court on your behalf.
Any answers given here do not indicate the existence of an attorney-client relationship between you and me, or between you and my firm. In order for such a relationship to develop, I must be admitted to practice in your jurisdiction, you and I must countersign a retainer agreement, you must pay my fee, and we must speak in confidence. If all of these conditions are not met, I am essentially answering a hypothetical for the purposes of discourse.