Basically it depends on your Irish Residence Status.
If you are in Ireland for 183 days in a tax year or,
are in Ireland for more than 280 days in any one year and the preceeding year you will be treated as tax resident in Ireland for each tax year, and taxable on your worldwide income in those years..
However, if you leave Ireland with the intention of remaining abroad and not being Irish resident in the following year, you can apply to have "split year treatment" - i.e. taxed in Ireland only up to the date of leaving Ireland in that tax year (only of you can satisfy the Revenue of this).
If you are in this situation, I would suggest that you get professional advice on this matter - I am available for consultation.