In 1125 he was elected by the monks of the Abbey of St. Gildas, near Vannes, Brittany (then, France now), to be their abbot, so he turned the Paraclete over to Heloise, who had been in a convent in Argenteuil since taking the veil. She became the Paraclete's abbess and spent the rest of her life there. She and Abelard are buried together there.
Paraclete comes from the Greek word meaning "one who consoles" and is found in the Gospel of John (16:7) as a name for the Holy Spirit, the name of the third person of the Trinity.