If you were born on the island of Ireland, your right to Irish citizenship depends on a number of factors.
Born before 1 January 2005
If you were born on the island of Ireland before 1 January 2005, you are entitled to be an Irish citizen.
Born after 1 January 2005
If you were born on the island of Ireland on or after 1 January 2005, your right to Irish citizenship depends on:
Your parents’ citizenship at the time of your birth
The residency history of one of your parents before your birth
This is due to a change in the legislation dealing with Irish nationality and citizenship.
Source: www.embassyofireland.vn