MNZ are affiliated to the FIA (the world governing body of motorsport).
MNZ have control of motorsport in this country which they maintain in various ways. They issue Track Licences for the circuits and Permits for events not held on circuits (hillclimbs, autocrosses etc). They then issue Competition Licences to individual competitors so that they can compete in MNZ sanctioned events. If an individual contravenes MNZ rules they can be disciplined in various ways including having their competition licence revoked. Competing in non-MNZ sanctioned motorsport events could result in disciplinary action. These are all "in house" methods.
Then there was the recent case where a group attempted to set up a 'rival' series (the V8 Supertourers). This ended up in Court and MNZ (i.e. every car club member) with a $800,000 bill.