Presuming you're planning on travelling soon (i.e. before any of the planned border changes in the next few months), my understanding is that you'll need to apply for a Request to Travel. In the link below, it states that partners of NZ citizens can travel to NZ but do require a form to be filled out.
The international border is open and eligible travellers are now able to apply for a visa.
www.immigration.govt.nz
I'm a Kiwi and my wife is an Aussie but we both live in NZ normally, so we were able to travel to/from AU the other week with relative ease and weren't required to fill out the Request to Travel form. However, if you don't live in NZ normally, I'd recommend filling out the form.
According to this link here, being a partner is considered a valid reason to travel (I think!), you just need to provide evidence of the relationship.
How to complete your application for critical purpose travel.
www.immigration.govt.nz