All new immigrants arriving into NZ MUST strictly adhere to the biosecurity procedures setup by MPI at the airports. These measures are in place to prevent introduction of unwanted pests, diseases, flora, and fauna into New Zealand. You will face HUGE fines, If you fail to comply with these procedures.
To be safe always DECLARE WHATEVER FOOD/EDIBLE/MEDICINE/PLANT/MEAT ITEM YOU HAVE!!!
More details can be looked up here:
Risky items:
Check with this tool whether you are allowed to bring an item into NZ: