There’s a helluva lot of red tape involved – and of course, fees.
You must prove to the Police that you are a “Fit and Proper” person, which means; no convictions, good character and referees who can attest to that.
Then you fill in the form.
Of course you must have a drivers licence, before you get your passenger service (passenger) licence.
You must demonstrate that you know all the law, all the geography of the area in which you intend to work, and can handle a vehicle with precision.
It may take 6 months.

If you are the owner of the vehicle being used, your must hold a passenger service (vehicle) licence too.
These vehicles are subject to very strict and rigid engineering and safety standards called a CoF. The dimensions between seats, between the floor and the seat, between the roof and the seat, between the seat and the side walls are all carefully measured to the millimetre. The brake drums or discs are taken off the vehicle and checked for wear. There must be a light or a buzzer on the dashboard that activates if a door is open. plenty more things as well.

The best way is to buy a vehicle already CoFd, rather than the usual WoF. Buy an ex rental or someone elses CoFd vehicle if you are buying second hand. Check with a new vehicle, as some can not be CoFd off the shelf, and modifications to them to bring them to the required standard may not be possible.
Check what vehicles are already certified.

Drive a shuttle is my advice, the work is alot easier and less stressful as you rarely have to deal with drunks and louts.
The difference between a taxi and a shuttle is that taxis have a point to point fare worked off a meter; shuttles have zonal fares – usually a price for the first person and then so much per head for each other person on the same trip going to the same address.

A taxi is an exclusive ride unless the first hirer gives the driver permission to take on extra passengers heading in the same direction; a shuttle ride is shared, unless the first person on pays a charge for the ride of a sum equivalent to what the driver would collect if the vehicle was full.

Most taxi or shuttle drivers can make a reasonable living, but you have to move in the the field of chauffeur before you start earning an above-average wage.

I’m not sure, but I think you have to be a New Zealand citizen.

Best of luck!
DriverT