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

Here is Why You Need An Adapter

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

Canary Islands

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

Type C

Type E

Type F

New Zealand

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

Type I