The President of Ireland (currently Michael D. Higgins) is addressed according to established diplomatic and state protocols:
Envelope/Outer Address:
His Excellency Michael D. Higgins
President of Ireland
Áras an Uachtaráin
Phoenix Park
Dublin 8
Ireland
Salutation:
"Your Excellency," or "President Higgins,"
"President Higgins" is appropriate. "Mr. President" is acceptable but less common in Irish practice than in U.S. usage. The Irish language form "A Uachtaráin" (vocative case) is used in official Irish-language contexts and ceremonies.
Unlike the U.S. presidency, the Irish presidency is largely ceremonial (head of state, not head of government). The Taoiseach (Prime Minister) holds executive power. Protocol reflects the President's role as guardian of the Constitution and representative of the Irish people.