His eldest son Donough was a minor when his father died and Connor's brother Murrough gained the estates and title of King of Thomond under tanistry, or popular election (then in general use, but abolished by King James in 1605) whereby the estate and title were to descend, for life, to the eldest and worthiest man of the blood and name of him that died last.
However, on the death of Donough in 1551, the rights of his son, Connor, 3rd Earl of Thomond, to the title and estates was challenged by Donnell, his uncle and a brother of his father, who was inaugurated O'Brien and chief of the Dal Cais.
After many years of family and civil strife Connor secured his position and lands in the late 1570s during the reign of Queen Elizabeth.
[5] Connor married Anabella, youngest daughter of Ulick De Burgh, (the red) of Clanrickard.
They had two children:[6][7] Connor's second wife was Ellice, daughter of Maurice née Baccagh, Earl of Desmond.