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

Here is Why You Need An Adapter

The outlet and plug type used in Ireland (Eire) is G and in Réunion are C and E. This is how they look like.

Réunion

In Réunion, outlets of type C and E are in use.

Type C

Type E

Ireland (Eire)

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

Type G