You Do Need power plug adapter while traveling from Isle of Man to Ireland (Eire).

Here is Why You Need An Adapter

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

Isle of Man

In Isle of Man, outlets of type C and G are in use.

Type C

Type G

Ireland (Eire)

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

Type G