The Irish state has not ever invaded or pillaged anywhere, but Irish individuals and clans certainly have. Irish raiders frequently raided coastal England, Scotland and Wales, sometimes creating settlements and spreading Irish culture and language.
The Fenians also launched an invasion of Canada in an attempt to grab land and influence after the American civil war; and whilst Ireland was a subject nation at home, Irish soldiers, missionaries, settlers, and administrators played major roles in colonizing, governing, and building territories abroad within the British imperial system.
Wasn't St Patrick kidnapped as a child from northern England/Scotland by Irish raiders and taken back to Ireland as a slave? After his escape - he returned to Ireland many years later in order to convert the Irish to Christianity.