You can cancel your Air New Zealand flight ticket by the following methods mentioned below;

You can cancel your ticket on the website by going to 'manage booking. ' After filling out the required details on the page, you will be taken to the summary page of your booking; the option for cancellations will be there. You can go to the option, proceed to the cancellation process, and confirm it.
You can also call Air New Zealand by dialling' 1800 262 1234'. After following IVR instructions, you will be connected to the customer service executive; you can request the ticket cancellation from them.
You can also visit the airport and request the customer service agent for the cancellation, and they will cancel your ticket.

What charges do I have to pay to cancel Air New Zealand?

You will have to pay a charge on domestic and international flights; the fee associated with cancellations under the Air New Zealand cancellation policy is $100 to $500 if the cancellation request is made after 24 hours of purchasing the ticket.

Will I get refund if I cancel my Air New Zealand flight?

Yes, you will get the refund, but there are some Air New Zealand refund policies that you must know;

The 24-hour cancellations policy is where you will get a full refund.
If you cancel your ticket after 24 hours of booking but follow the Air New Zealand refund policy rules, the points will be redeemed on your next flight within 12 months.
If you have a refundable ticket, the airline will provide a full refund before the departure.
You will be refunded if you fly from a specific country within the state that requires the airline to refund you fully.