What if you are still waiting for a test?
Starting the swap does not stop the clock, but it does not have to. You may keep driving on your own licence right up to your deadline, even while you wait for a test date. What you cannot do is drive past that deadline just because the booking system is busy.
This is exactly why the 1 November change matters so much. Test slots are already hard to get. If your window shrinks by six months, the queue you were relying on may no longer fit inside it.
Does the licence itself need to be current?
To keep driving, yes. To swap it, you have a little room: New Zealand accepts a licence that ran out within the last 12 months. Older than that and the swap is off the table, whichever country you are from.
Many people reach this page while sorting out a visa at the same time. If that is you, sending everything at once is far cheaper than sending it piece by piece — our immigration document translation page explains how a combined order works.