Property Law Act 2007, ss 332(b), 335(1), 336(2), 337(1)-(2)
Like all issues with neighbours, it’s best to talk to your neighbour first to see if you can work out a solution. If that doesn’t work, you can apply to the District Court for it to order your neighbour to trim or remove the tree. In this context, “tree” here includes any kind of shrub or plant.