You Do Need power plug adapter while traveling from New Zealand to Canary Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Canary Islands are C, E and F and in New Zealand is I. This is how they look like.

New Zealand

In New Zealand, outlets of type I are in use.

Type I

Canary Islands

In Canary Islands, outlets of type C, E and F are in use.

Type C

Type E

Type F