Hi Winglet,
If you have NZ
PR then Air NZ is an option. However the only entry points for the airline are B733 first officer and wide body second officer B777, B767 and B747 (no flying below 10,000 or transition)
The B744 will be phased out over the next 4.5 years and a large number of current B744 Captain, First Officers and Second officers have been down trained to the B777 as of next month.
All the application details are on the Air NZ website, so spin the dice and have a go, if that what you want to aim for.
Good Luck