Wiktionary
n. (label en Ireland history ecclesiastical) the head of a clan occupying church lands under a bishop in Gaelic Ireland
Wikipedia
The medieval Irish office of erenagh was responsible for receiving parish revenue from tithes and rents, building and maintaining church property and overseeing the termonn lands that generated parish income. Thus he had a prebendary role. The erenagh originally had a tonsure but took no other holy orders; he had a voice in the Chapter when they consulted about revenues, paid a yearly rent to the Bishop and a fine on the marriage of each daughter. The role usually passed down from generation to generation in certain families in each parish. After the Reformation and the Dissolution of the Monasteries the role of erenagh became subsumed in the responsibilities of the parson in each parish.