New Zealand could be in trouble if ocean acidification happens or weather patterns cause more drought (~80% hydro for energy generation and the arable land relies upon high rainfall).
Can there even be non-localised drought on a small island the size of New Zealand? The only significant geographical feature in the North Island (where most people live) is 3 mountains right in the middle.
New Zealand is small enough that a localized drought can have significant impact. Most of the people do indeed live in the North Island but most of the power is generated in the South Island, particularly around the Mackenzie Basin/Otago area (dry highlands).