How did tuatara come to new zealand?

Answer 1

The Kakapo brought itself, presumably in the shape of a predecessor that still could fly some time way back when.

Exactly how no one knows, but presumably through birds being swept away from the mainland by storms.

Answer 2

The ancestors of the Tuatara originated about 200 million years ago, as a sub-species of the broad dinosaur family, and probably arrived via land bridges which are long gone. The route is probably that used by other NZ fauna, such as Kiwi.