On the death of the previous ceann fine, his brother Domhnall an Saithnech Mág Tighearnán in 1312, Conchobar took the chieftaincy and resided in the castle of Croaghan of the Cups (Irish- Cruachan O'Cúbhrán), now in the townland of Coolnashinny, besides the modern town of Killeshandra.
The Annals of Ulster for 1314 state- Conchobur Mag Tighernain 'the Tawny', chief of Tellach-Dunchadha, was slain in the defeat of Cell-mor and Mathgamain Mag Tighernain and the Red Gillie, son of the Herenagh and many more of his tribe and Nicholas Mac in Maighistir and many of his sept were slain.
The Annals of Connacht for the year 1317 state- Defeat of Mac Ruaidri and the men of Brefne at Kilmore.
The Annals of Loch Cé for the year 1317 state- The victory of Cill-mor over Mac Ruaidhri and the men of Breifne; and seven score gallowglasses of the son of Ruaidhri's people were slain there; and Aedh Breifnech O'Conchobhair's two sons were taken prisoners there; and Donnchadh, son of Niall O'Ruairc, and Conchobhar Buidhe Mac Tighernain, chieftain of Tellach-Dunchadha, were slain there, and Mathghamhain Mac Tighernain, and the Gilla-ruadh, son of the Airchinnech Mac Tighernain, and Nicholas Mac-in-Maigistir, and many more of his kindred besides.
The Annals of Clonmacnoise for 1317 state- The overthrow of Kilmore was given upon mcRory & breifnie men, where 150 Gallowglasses belonging to mcRory were killed, & the sone of Hugh Breifnagh o'Connor was taken Captive, the 2 sones of Neale o'Roirk and Conor Boye mcTyernan cheiftaine of TeallayDonoghoe were killed, Mahon mcTyernan, Gilleroe mcAnarchinny, Nicoll mcen Maister and many others of that familie were alsoe killed.