If wanting to cross Cook Strait (North Island ~ South Island[the mainland]) check carefully if doing a one way hire.
Some will want you want you to swap cars at Wellington ~ Picton. Others will allow and some do not allow.
With one way hire are always surplus of cars at southern depots. Many people drive south and fly north.
Hence (are others)
Relocation rental cars, campervans and motorhomes | Transfercar
As well as the international majors, are local car rental companies.
Omega Rentals
https://www.apexrentals.co.nz/
Ezi Rentals Was know as A2B Car Rental
Snap rentals
You may pay a premium to rent from the airport. Renting from a city location may be a lot less, for the small cost of a taxi/uber from the airport to the rental car location.