The Uí Dúnchada dynasty held an important ecclesiastical role within the triumvirate, the Abbacy of Kildare, and Muiredach was simultaneously abbot and Kings of Leinster. The Uí Néill clientship dates to 806 when High King Aed Oirdnide mac Néill invaded Leinster and deposed Finsnechtae. Finsnechtae regained the kingdom, presumably with Uí Néill support until his death in 808 causing dynastic strife and a further invasion of the High King.
The Uí Dúnchada dynasty held a significant religious position within the triumvirate, the Abbacy of Kildare, and Muiredach served as abbot and King of Leinster simultaneously. The Uí Néill client relationship dates back to 806 when High King Aed Oirdnide mac Néill invaded Leinster and deposed Finsnechtae. Finsnechtae regained the kingdom, possibly with Uí Néill support until his death in 808, leading to dynastic conflict and a further invasion by the High King.