You Do Need power plug adapter while traveling from Nauru to Ireland (Eire).

Here is Why You Need An Adapter

The outlet and plug type used in Ireland (Eire) is G and in Nauru is I. This is how they look like.

Nauru

In Nauru, outlets of type I are in use.

Type I

Ireland (Eire)

In Ireland (Eire), outlets of type G are in use.

Type G