If the no contact order is part of a criminal case, such as an order for protection violation or an assault, it usually gets dropped at the close of the case (when the defendant pleads guilty or the case is dismissed). Keep in mind that each case is different and there may be an instance where a no contact order is maintained during the entire duration of the defendant's probation.
If the no contact order is an interim condition while a criminal case is still pending, it is possible to have the order lifted, typically with the consent of the alleged victim who contacts the court liaison, victim advocate or the prosecutor expressing such a wish. A defendant can ask for the no contact order to be dropped over the alleged victim's wishes but a judge is highly unlikely to grant the request. If the alleged victim is on board with dropping the no contact order, the chances of the judge agreeing a much better but it's still the judge's discretion.
If you cannot afford a private attorney, I recommend applying for the services of the public defender's office, speaking with a panel attorney who may represent you at a reduced fee or finding a lawyer in your area who is willing to apply some pro bono hours to your case to lower the overall representation fee.