Definitely. Below the Maraetai dam where it enters the top of Lake Arapuni is renowned for big trout. I have seen a huge brownie that would have been well into double figures cruising right against the concrete wall. i have got rainbows around 7-8lb a few years ago when i fished it regularly. At times, you'll see thousands of smelt/whitebait, hence the trout. Due to the lack of back room, use a spinning rod with a small ball sinker, 1m 8-12lb trace and a popular smelt fly. Stand on the concrete structure accessed from the carpark, cast up/across as far as you can, left the rig drift downstream, keeping in touch with the fly. Bang. or no takers, wind in fast when the line reaches directly below you. I never saw a fish caught on the wind in. They typically take at about 3/2 o'clock if 12 is directly below you.
You'll snag the bottom a bit, but it's worth it.
don't leave valuables or fishing gear obvious in your car, there.
Also way down at the bottom of the lake off Arapuni Dam face, same rig into the deep still water. And the road bridge nearby that crosses the outlet of Arapuni, cast upstream and the fly drifts back towards you. But you need a way to land the fish (locals use some genius net contraptions).
Also, I've fly fished the shoreline of the lake, out over the obvious weed beds with a nymphing rig, got some nice fish. But not as productive as the top or bottom of the lake.
Get hold of a Fish & Game brochure on the area.