You Do Need power plug adapter while traveling from Turks and Caicos Islands to New Zealand.

Here is Why You Need An Adapter

The outlet and plug type used in New Zealand is I and in Turks and Caicos Islands are A and B. This is how they look like.

Turks and Caicos Islands

In Turks and Caicos Islands, outlets of type A and B are in use.

Type A

Type B

New Zealand

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

Type I