The way I understand it from people working in the field, is that the issue isn't really that lakes/rivers are running dry, but more that most hydropower is produced on the South Island while most consumption is on the North Island and the connection is woefully inadequate (typical NZ problem, never invest in infrastructure just keep bandaiding it). That said installing wind and solar (both of which are plentiful) would do a lot towards alleviating the problems, but there are the issues of the existing generators lobbying and the political climate, where the conservative party still has a significant number of politicians who think climate change isn't real.
The issue is that we have insufficient extra generating capacity during a dry year. At the moment we don't have enough [gas] to fully use all our existing thermal plant in a dry year. There are no projects in the generation pipeline that would provide backup energy to cover dry years.
A lot more solar would help, but the government owned generators are knobbling private investment through dirty tactics (the details are not public - I got this from a planned utility scale solar farm that is being cock-blocked). Fundamentally the issue is that the generators make more money by preventing extra generating capacity coming online.
Don't blame "the conservative party": Labour were also completely useless when they were in power (admittedly National still isn't helping). Politicians rabbit on about infrastructure investment e.g. the link I gave that mentions the pumped hydro scheme backed by Labour and cancelled by National because it was uneconomic. Both parties wastefully "invest" in infrastructure, and both make stupid decisions to score political points rather than solve problems sensibly. It's nonsense to blame one party. Both parties are preventing utility scale solar installations (indirectly).
Climate change isn't the cause here - your bias is showing.
Even Australian politicians and their regulator have managed to sort it out. New Zealand is just fucking it up.
