The formal, legal, official process behind the appointment of a new Reserve Bank of NZ Governor is enshrined in legislation which says that its the RBNZ board which must make a recommendation. It can be accepted or rejected by the Minister of Finance. Should it be rejected, the Board must look for another candidate. Should it be accepted, the Finance Minister must consult with other political parties, and then make a final recommendation to the Governor General. The entire point is to ensure Central Bank Independence from partisan politics. Upon the Board conducting its own independent search for the best person, it becomes very awkward for a Finance Minister to reject that candidate. Even should they do so, the Minister still has no control over the next one who is proposed by the Board. Politics is thereby kept to a minimum. How nice in theory. Especially when first, a former Minister of Finance, and second, one of the highest profile current political leaders in NZ, told me that is not how it works in practice.
So how does it? The former Finance Minister said that a chat occurred between them & the RBNZ Chair to arrive at a mutually agreeable candidate. Lovely, but not constitutional. After the meeting, the Bank Chair knows that the candidate who they will propose will in turn be accepted - thereby avoiding embarrassment all round. In sport, they call it "match fixing". But this is NZ, after all, so everything has to be pleasant & everyone has to get along. No room for trouble makers & disruptors, especially "radical" ones. Yes the actual appointments process is completely different from the legal one. Instead a committee of two people, the RBNZ Board Chair & Finance Minister, together decide who will be the next Governor, by unanimous vote. Nothing like that process appears in a single official document.
My second source is a conversation back in 2017 with a person who is now a super prominent Minister in the current Coalition Cabinet (not a Nat). Labour had just won the election under Ardern. They were in the process of appointing a new Governor. I discussed the matter with him & referred to the Board making a recommendation. He said, "If you think its the Board of the Reserve Bank that appoints the Governor, then you must be joking". I took the line to mean how it was intended - that the Governor is chosen by the Finance Minister - and any pretense otherwise is laughable. It only tricks fools like myself (and 5 million other Kiwis). Lets trust that under Finance Minister Willis it will not be a stitch up.