Depends on the product. Our manufacturing base has been gutted by laissez-faire capitalism (Mondelez and the Cadbury factory being a recent example https://www.stuff.co.nz/business/103965900/popular-dunedin-a...), so most heavily processed foods are imported from Australia.
And 1 of the 2 supermarket chains (Progressive Enterprises) in our cosy duopoly will import other foods from Australia as suits them - but that's because they're an Australian firm and offload excess stock to the NZ market.
In terms of vegetables, fruit, meat, dairy products etc., they're only imported when there's a margin in doing so - for example, we used to have a lot of cheap pork from overseas countries that didn't have to adhere to the same animal welfare practises as local pork producers.