No. The Republic of Ireland is a republic, which means it does not have a monarchy. It has a president. Northern Ireland has the Queen as its head of state.
Ireland is a republic, so it does not have a queen. Ireland has a president. Northern Ireland comes under the jurisdiction of the United Kingdom and it has a queen.
Northern comes under the rule of Queen Elizabeth 11, Queen of England.
The English wanted Ireland to be under its control. Ireland didn't want to be under control.
Northern Ireland is separate to the Republic of Ireland. The Republic of Ireland has a president. Northern Ireland comes under the jurisdiction of the United Kingdom which is not a republic, but a monarchy and so it has a queen.
When Elizabeth I was queen of England, Ireland would have been under British rule. She was also queen when the Ulster Plantation happened, a significant event in Irish history, where lots of people were moved from Britain to Ireland taking land from people who were living there.
Ireland
The term for a colony under direct control of the English King or Queen is a royal colony, or crown colony. The colony is ruled by a governor appointed by the Monarch.
Royal Colony is the term for a colony under direct control of the English king or queen. Before the Revolutionary Wars, there were several Royal Colonies in North America.
Firstly, Northern Ireland uses the British Pound Sterlingwhilst the Republic of Ireland uses the Euro. Secondly, Northern Ireland is under the rule of the Monarch in England (currently Queen Elizabeth II) whilst the Republic has a president. Also, on maps there is a clear divide between both the Republic and Northern Ireland. Of course, there are several more pieces of evidence of this partition, such as visible things like road signs looking different.
Ireland became independent and a republic. They were under British rule, which was a monarchy and so had a king or queen. A republic has a president. So when Ireland became independent they eventually started to have a president as the head of state.
Because King Henry II invaded Ireland under authorisation from Pope Adrian IV and declared himself to be "Lord of Ireland." Ireland has been under English authority ever since and the English at one stage tried to stamp out Irish culture and customs altogether. Also, English unwillingness to help during the great potatoe famine(s).
Queen Elizabeth isn't a system, she's an individual. Queen Elizabeth II is the Head of State of the United Kingdom of Great Britain and Northern Ireland under the system of a Constitutional Monarchy