You Do Need power plug adapter while traveling from Northern Ireland to Saint Barthélemy.

Here is Why You Need An Adapter

The outlet and plug type used in Saint Barthélemy are C and E and in Northern Ireland is G. This is how they look like.

Northern Ireland

In Northern Ireland, outlets of type G are in use.

Type G

Saint Barthélemy

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

Type C

Type E