Even after a New Jersey divorce ruling has been entered, both parties are not free from the jurisdiction of the family law court. The provisions of the divorce agreement remain effective, and the two ex-spouses must continue to abide by the ruling of the court. If not, they can be found in contempt of court.
Practically any part of the divorce decree can lead to a contempt filing. Certainly, matters of custody and child support continue to be subject to the court. Any failure to pay support or make the children available for visitation can get one parent in legal trouble. The decree is more than just a piece of paper. It has the force of law that each party must follow. If not, they can be fined or even sent to jail.
If one feels that their ex-spouse has violated the divorce agreement, they can file a motion for contempt with the court and receive a hearing. The motion would detail what the spouse believes the other did wrong that deserves punishment. Note that contempt of court is a drastic remedy due to the penalties, so the violation would have to be very serious for the judge to grant the motion. The party filing the motion for contempt would need to prove that the other party did something that merits a harsh punishment.
Someone who feels that their ex-spouse has broken the divorce agreement could contact a divorce attorney to learn more about when they can file a motion for contempt. The flip side of this is that judges will not like it when one files for contempt without very serious justification. Thus, one should consult with a lawyer to see if contempt is the appropriate action or whether a modification of the divorce agreement is better.