Hunting is a traditional activity among Pakeha farmers and farming communities in Aotearoa. These people came from lower and middle class British communities, and enthusiastically began hunting in Aotearoa because in Britain it was traditionally an upper-class-only privilege. As such it is and has always been primarily been a leisure activity. Nowadays Pakeha culture is strongest in rural areas so the hunting continues and is part of a grid of activities (rugby, agricultural shows, many varieties of sport, other farming-centric activities) which strengthen in-group bonds.

Maori hunted extensively for subsistence, primarily bird and fish species, but this was more trapping and gathering (rope traps for birds, gathering bivalves). In recent times their culture has become more urban-based, relatively young and lower SES, and I think they are more involved and interested these days in urban family/community ties, Marae activities, travel and international youth culture. Maori groups promote the traditional ecology of the islands, and promote the authenticity of traditional Maori food-gathering, but especially given the scarcity of native birdlife, don't actually hunt birds anymore (as far as I'm aware - though shell-gathering is popular).

The university-liberal segment of Pakeha culture that is pro-Maori is generally pretty pacifist and urban, so they don't participate in rural-centric activities like hunting.

I think Maori people in Aotearoa taking up white-style hunting would be like native tribes in America turning into massive baseball lovers.