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Glúniairn was a son of Amlaíb Cuarán (d. after 980) who abdicated as king of Dublin following his defeat at the Battle of Tara in 980 and the subsequent capture of Dublin by Máel Sechnaill mac Domnaill of Clann Cholmáin, the High King of Ireland. Olaf retired to Iona where he probably became a monk and later died. Glúniairn and Máel Sechnaill were both sons of Dúnlaith, sister of the previous High King, Domnall ua Néill of Cenél nEógain, and Máel Sechnaill appointed his half-brother to rule in Dublin as his client. Máel Sechnaill removed many of the hostages and captives that Amlaíb Cuarán had held in Dublin, including Domnall Clóen, King of Leinster.