Coarb

A coarb, from the Old Irish comarbae (Modern Irish: comharba, Latin: hērēs), meaning "heir" or "successor", was a distinctive office of the medieval Celtic Church among the Gaels of Ireland and Scotland. In this period coarb appears interchangeable with "erenach", denoting the episcopally nominated lay guardian of a parish church and headman of the family in hereditary occupation of church lands. The coarb, however, often had charge of a church which had held comparatively high rank in pre‐Norman Ireland, or one still possessed of relatively extensive termon lands.

Also as per this article "... such lucrative monastic offices as “coarb” (comarbae “heir” to a saint) or “erenach” (airchinnech “superior”), otherwise transmitted by natural or nepotic descent within ecclesiastical families, which were often the politically displaced branches of royal dynasties"