Opinion regarding technical resignation

Already you have tendered your resignation and it is accepted. You will be relieved as agreed and mentioned your technical resignation acceptance letter and they will give you the relieving certificate.
Now you have to wait for the appointment order. Till you get that you can't join in the new job. I think you can spend time waiting for an order for the new job.
You can discuss with the present employer and ask him to help you if there is any way for extending your relieving date from the present job,

The first part of your problems is solved as your technical resignation is accepted. You have not made it clear when you are being relieved. If they relieve you at a later period in view of the delay of joining in the new post then you have to continue working here till further developments in the matter.

Govt agencies take their own time in these things as they have to follow certain procedures. Still if you have a feeling that matter is being delayed more than the stipulated period then you can find out from that department about this bottleneck. If your doubt is proved true you can even request the higher ups there to accelerate the process citing that you will be loosing in your seniority or salary difference between the new and old job etc. Sometimes pursing the case in humble ways also helps to mitigate the bottleneck situation.