Well, that just happened. And once the body is buried, its time for politicians to fulfil their promise and let us make the move.
Obviously, such a change would need to be endorsed by a referendum, so the process will take a couple of years. As for the nuts and bolts, Dean Knight helpfully provided a guide for the minimal reform - which changes nothing while changing everything - in his 2020 paper A Republic for New Zealand: A Possible Blueprint in the Tradition of Minimalist Reform. That would rid us of the foreign monarchy and replace the appointed Governor-General with a government-nominated, Parliament-endorsed Head of State, clearing away the royalist baggage without the distraction of other issues, and leaving us free to decide what other changes we might want to make later.
The archaic ideology of monarchy is completely at odds with the values of modern, democratic Aotearoa. And now the incumbent is dead, it is finally time for us to move on.