You Do Need power plug adapter while traveling from Saint Kitts and Nevis to Nauru.

Here is Why You Need An Adapter

The outlet and plug type used in Nauru is I and in Saint Kitts and Nevis are D and G. This is how they look like.

Saint Kitts and Nevis

In Saint Kitts and Nevis, outlets of type D and G are in use.

Type D

Type G

Nauru

In Nauru, outlets of type I are in use.

Type I