On the death of the previous chief, Gíolla Íosa Mór Mág Tighearnán in 1279, Duarcán 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 1290 state Duarcan Mac Tigernain, chief of Tellach-Dunchadha, rested in Christ.
The Annals of the Four Masters for 1294 state- Duarcan Mac-Tiernan, Lord, or Chieftain, of Teallach Dunchadha, died.
The Annals of Loch Cé for the year 1293 state- Two chieftains of Tellach-Dunchadha died in hoc anno.
Duarcán had a son Sithric Mág Tighearnán, who succeeded him as chief of the clan.