Hard to identify the major industries. I guess Kiwi wines are a thing, but tariffs may cut their popularity in the US. (BTW I saw that US wine imported to Canada is down more than 90%. Whoda thunkit?) Phosphate mining? Healthcare? Is it still true there are more sheep in NZ than people?
NZ is expected - and I believe it has been confirmed at based on the news last night but with the US ATM who knows - to get a 10% across the board tariff which is the lowest world-wide rate as I understand it. So while NZ selling prices for its exports to the US will rise, NZ in general is in a comparatively good place as its competitor exports will also rise the same or more. And so NZ is in a relatively OK place in that while the US is the #2 export partner, on a world scale its exports aren't that large (in volume terms) and as a result NZ is relatively easily able to pivot elsewhere where it makes sense most likely further into Asia.

And so the burden of this (bilateral) change will IMO most likely fall on the US as 1) the US consumer will need to fund the tariffs (or the export good will go elsewhere) and 2) NZ will look to move more of its 'strategic' large purchases (commercial aircraft, defense etc.) to less capricious partners that are more aligned on key issues like climate change or rules-based international relations than the US currently (as an example those two issues are critical for NZ). And - like a lot of the Pacific - NZ could fall further into China's already considerable influence, although the EU, UK, Canada, Japan etc. have already indicated they'd like (even) deeper ties as those countries / regions are looking to urgently manage their own tariff issues.

In terms of significant industries to invest. Dairy (Fonterra, A2 et al) is a huge thing for NZ. NZ is circa 30% of the world's dairy export market (most dairy production is for domestic consumption) but also forestry, agriculture (Zespri, NZ apples etc.) , increasingly mining. However where NZ companies have typically appeared as good value investment worthy companies is generally NZ Telecom, Fonterra / A2 etc., the banks (who are massively profitable & mostly Australian owned and so may be better accessed through investing in Australia), the energy companies (NZ is mainly renewable energy largely hydro but also with huge wind / solar resources and so somewhat limited investment with good & growing returns) & retirement. Raw returns might only be OK however there is potential for a double dip in that the raw return may be fine & then one might get a further leg up on the fx change.

And yes there are still more sheep in NZ than people. It's not as bad as the past when there might have been just under 60M sheep for 3.5-4M people (1990-ish). Today it's around 23.5M sheep for 5M people. Dairy & forestry have been the main improvers as the returns for those activities have generally been greater for farms in areas where all activities are possible, but the recent efforts to market NZ Merino wool have helped sheep-based returns lately I believe.