Quiting old job and joing new job.

Yes .You were suppoused to apply for the job with the permission of of your employer that too bein in a Govt. Job.

You must get NOC or you will be introuble in future. 

It is also necessary that you should inform facts in your application, and in all such notifications, there is a column that states Whether employed, If government employee, apply through proper channel etc. As you are working in the court itself, take all precautions and your Supdt can guide you better, and if NOC is required then present it as you may get credit of your completed service also, if the completed service is negligible and NOC was not insisted just forget the issue and resign the job.  But you have to contact the future employer and should confirm whether NOC is necessary for joining or not.

NOC is a matter of procedure; but not a mandatory requrement. In public service, it is sufficient if the employee gives while applying for jobs through PSC, SSC etc.

In the instant case, you my quit and join the new job. However, if you arre joining another Government job past service would not be counted unless the procedural requirements are followed.