Yes, you will be issued with an interim visa.
https://www.immigration.govt.nz/new-...t/interim-visa
You won't be allowed to attend work until your visa situation is sorted out, but there is no need to resign. As to how to go about it, you will have to talk to your employer to see what arrangements they are willing to have with you. I presume you have told them that you have to get another visa. And an employer such as a local council will know about not being able to work without that. Have you asked them if they are willing to hold the job for you in the meantime?
Your boss could try writing to them. I have heard of that making a difference, but ONLY ONCE, on the forum. Mostly, INZ work on date-order queues. I would try, too, but don't be surprised if you still have to keep waiting. Good luck.