An aspen in New Zealand? Wow, they travel far...
I wish I knew, I'm only familiar with our trees locally, as a landscaper. :/
Edit: Initially, it looked like a ficus to me, lol. But if it's native to New Zealand, it isn't a ficus. As far as I know, you don't have any native ficus trees.
After looking through a list of broad leafed trees native to New Zealand, I couldn't find anything similar, lol.
It drives me crazy when I can't figure out what a a plant is... lol. xD
Your best identifying features when you go to the nursery would be (including the leaf/branch sample): flowering/non-flowering; colour of flower; fruit producing/non-fruit producing; and bark colour