Entry extracted from the book The Plantagenets 
Since the early Middle Ages, the figure of the High King existed in Ireland, although the island was divided into independent kingdoms (Connacht, Ailech, Airgíalla, Ulster, Mide, Leinster, Osraige, Munster, Thormond). This position of Supreme King was not actually a position that supposed a real exercise of power over the rest of the country's monarchs, but rather it was a symbolic figure who received a ceremonial homage as a feudal lord from the rest of the kings, who maintained the independence of its power within its own borders. In any case, the degree of effective power exercised by the Supreme King in the rest of the country depended on the personality and strength of the man who held the position at any given time.
In the year 1166 the title of Supreme King of the country was disputed by the kings of Leinster, Diarmait MacMurchada, and of Connacht, Rory O'Connor. After being beaten by O'Connor, Diarmait suffered an even more humiliating defeat; His attempt to kidnap the daughter of a local chief named O'Rourke failed when he took up arms against him and managed to seize his land and his kingdom.
Seeing all was lost, Diarmait traveled to England and asked the English King Henry II to help him recover his throne, but he was not in a position to undertake the task at that time. Even so, he gave her a document in which he authorized her to recruit mercenaries among the English forces. The Irish king addressed the Norman lords fighting on the unruly Welsh frontier. His offer immediately aroused the interest of soldiers, petty nobles, and fortune seekers of all kinds, so he quickly recruited a sizeable force made up of English, Welsh, and Flemish (who had been in England since the civil war between King Stephen and Mother of Henry II, Matilda). The English forces that arrived with Diarmait in Ireland in 1167 were therefore not originally an army sent by the king, but a group of mercenaries
A key figure in the success of this invasion would be the Norman Richard fitz-Gilbert de Clare, who was known by the nickname of Strongbow. He had inherited the title of Earl of Pembroke from his father, but lost it in the aforementioned war between Stephen and Matilda. This is why he was so interested in the adventure, since in reward for his services, and if he succeeded in returning the kingdom of Leinster to him, Diarmait promised him the hand of his daughter Aoife and appoint her as his successor when he die.
De Clare joined the army that invaded Ireland in 1170 with about a thousand foot soldiers and about two hundred knights. Soon almost all of Leinster and much of eastern Ireland (including Dublin) came under Norman rule. Strongbow married on August 23, 1170, the daughter of King Diarmait; when he died in 1171, De Clare took over the inheritance that had been promised to him; he was in a position to form a practically independent Norman domain in Ireland.
Faced with this risk, Henry II reacted by organizing a conquest expedition to Ireland with an army of four thousand soldiers, of which more than five hundred were knights. There was another factor that led Henry to undertake the conquest of Ireland. The assassination of Thomas Becket was very recent, for which the English king was unanimously considered responsible. As part of the penance imposed on him, the pope ordered him to conquer Ireland, whose population was more than reluctant to renounce the traditional rites of the Irish church and submit to the dictates of Rome.
A fleet of four hundred English ships led by the king himself landed in Ireland, specifically at Waterford, on October 17, 1171. He reached Dublin, where he obtained the submission of the Irish and Norman lords, including De Clare whom he first dispossessed and then appointed as Lord of Leinster (thereby making it clear that from then on any title he held in Ireland would be by express grant of Henry II of England and not by his own conquests). This done, in April 1172 Henry returned to England, leaving Strongbow as his representative in Ireland.
This initial task of conquest was followed by a period of English colonization and settlement in Ireland. English laws and institutions were introduced (later an Irish parliament would be established in the image and likeness of the English), and castles (first of wood and then of stone) and both military and commercial settlements were built. High King Rory O'Connor's efforts to expel the invaders were in vain; he was turned away and forced to stay on his holdings west of the River Shannon. Finally, by the Treaty of Windsor (1175), O'Connor renounced his position as High King of Ireland and returned to being only King of Connacht, recognizing Henry II of England as his sovereign lord (two years later Henry appointed his son John Landless High King of Ireland). In 1186, the English, ignoring the treaty, deposed O'Connor and occupied Connacht.
As for de Clare, he demonstrated his loyalty to Henry II by fighting alongside him in Normandy in 1173 before returning to Ireland as royal governor. He spent the rest of his life fighting Irish rebels until he died in 1176. From his marriage to Aoife McMurchada a daughter was born, named Elizabeth de Clare. When she was orphaned, she moved to England where she lived in the Tower of London as a ward of the King of England until Richard the Lionheart granted her hand to William Marshal, considered the best knight and star of tournaments at the time.
The couple spent long periods on the extensive land inherited by the Marshal on behalf of his wife in Ireland (Elizabeth's only brother died as a child), which would cause serious problems during the reign of Juan sin Tierra... but that's another story.
The concurrence of circumstances arising from Diarmait McMurchada's request for English aid, Richard de Clare's expedition and Henry II's invasion in the face of the risk that he would establish a Norman kingdom independent on the island, is considered by many in Ireland as the origin of the historical problems between the two British islands.
Font| Lelia Ruckenstein and James O'Malley. Everything Irish. The History, Literature, Art, Music, People and Places of Ireland, from A to Z . Ballantine Books (2005).