Thank you for the question. In order to bring a claim for contempt of court, you will require a court order to have been broken, if there was a court case and it was subsequently dropped, then no order would have been made and therefore broken. IF however a court order has been made and the terms of this have not been met, at this point you can intimate proceedings for contempt. Usually if the person starts to comply after the application, you can pause the matter to be resumed should it be breached again.
I shall provide you with a helpful link that will assist you in finding a solicitor/representative near your local area. This will provide you with someone nearby your area who can assist you if required.
I hope this information proved helpful. You will find a local solicitor who deals with these matters on the law society webpage which is as follows;
https://www.lawsoc-ni.org/solicitors (N. Ireland)
Hopefully, I have answered your query in a way that is simple and easy to understand. If anything remains unclear, I will be more than happy to clarify it for you. In the meantime, thank you once again for using our services.
Should you require any further assistance on this matter, please do not hesitate to post a further questions for additional assistance.