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

Here is Why You Need An Adapter

The outlet and plug type used in Nauru 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

Nauru

In Nauru, outlets of type I are in use.

Type I