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

Here is Why You Need An Adapter

The outlet and plug type used in Ireland (Eire) is G and in Cayman Islands are A and B. This is how they look like.

Cayman Islands

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

Type A

Type B

Ireland (Eire)

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

Type G