The short answer is yes. In 1167, Diarmait Mac Murchada was deposed as King of Leinster (one of the four provinces of Ireland centered around Dublin) by the High King of Ireland Rory O'Connor. To get his kingdom back, he invited Richard de Clare (aka Strongbow) and several Norman warriors to help him get his kingdom back. Unfortunately, Strongbow betrayed Diarmait Mac Murchada and established their Norman kingdoms in Leinster and the surrounding areas. This was the point in which the Pale (an Norman-English enclave) starts to develop around Dublin. In 1171, the English king Henry II decided he wanted to put these Norman areas under his control and is angry that they have broken away from him. Strongbow surrenders to him and the English crown established a nominal control. This means that the English crown becomes a presence within the Irish political environment. The local chieftains would have to treat with English officials periodically. English laws also got passed inside Ireland that forced a degree of interaction with the English state.

The majority of the actual conquest of Ireland takes place under Elizabeth I and James I. Both had extensive contacts with the various Irish chieftains and tried to get the Irish swear fealty in exchange for English titles over Irish land. This built upon established precedents of earlier dynasties, but the Tudors and Stuarts expanded it. This policy was termed "Surrender and Regrant" and was partnered with the plantation system centered around Ulster and other English-controlled areas.

Sources

Falls, Cyril. Elizabeth's Irish Wars. New York: Barnes & Noble, 1970.

Kane, Brendan Michael. "Making the Irish European: Gaelic Honor Politics and Its Continental Contexts". Renaissance Quarterly. 61, no. 4: 1139-1166.

Robinson, Philip S. The Plantation of Ulster: British Settlement in an Irish Landscape, 1600-1670. New York: St. Martin's Press, 1984.