Country code top level domains are delegated by IANA to some managing entity. With a new ISO 3166-1 alpha-2 code, a legitimate claim, and evidence of competently running a DNS server, a new delegation could be made to start a new one. Probably to the same manager of the old name, but that is not a sure thing. Delegation being the key word, because IANA does not control what managers do with their zones, only what is in the DNS root.
.nz currently is administered by InternetNZ. Their activity report shows them tracking just under 725,000 names. But no mention of tracking a new TLD in their planning. Whether it has yet to come to their attention, or a new entity will manage Aotearoa's TLD, or this won't actually end up happening, I don't know.
Timing and nature of the transition isn't really a technical question. If the government says .aa is open for business and .nz will someday be deleted, better plan for that when securing domain names.
Doing DNS magic at the ccTLD level has its limits. Granting the existing domain customer example.aa may save the trouble of registering it. However, your zones and TLS certificates all are example.nz.
Some interesting precedents. .zr was deleted in 2001 some years after the Democratic Republic of the Congo was renamed. In contrast, .su outlives the fall of the Union of Soviet Socialist Republics.