My guess is that they would do an SQ and form a separate offshore company and any EK driver who wanted to move to AKL would have to resign from EK and start again with the separate company with that company's 'package', whatever that may be.
And given the low wages Kiwi pilots seem content(?) to receive, I'd also be guessing that EK would be looking to employ as many pilots from that part of the world and not currently employed by EK as possible, DECs and well as FOs.
But that's just my guess.