Ireland as a whole is not represented on the Union Jack. The flag—officially the Union Flag—symbolizes the union of the kingdoms of England (including Wales) and Scotland. The current design, dating from 1801, incorporates the red cross of St. George for England, the white saltire of St. Andrew for Scotland, and the red saltire of St. Patrick for Ireland.
However, the St. Patrick's saltire represents the historical Kingdom of Ireland, not the modern sovereign state. Today, only Northern Ireland remains part of the United Kingdom. The Republic of Ireland is an independent country and has no representation on the flag. Wales, despite being a constituent nation, is not separately represented because it was legally incorporated into the Kingdom of England prior to the flag's creation.