The Genealogia Fundatoris of Coventry Monastery names “Algarus tertius” as son of “Leofricus tertius”. Florence of Worcester records that he was created Earl of the East Angles in 1053, in succession to Harold, son of Godwin, who had succeeded his father as Earl of Wessex. Florence of Worcester also records that Ælfgar was banished in 1055 by King Edward "without any just cause of offence". He went to Ireland, then to Wales where he allied himself with Gruffydd ap Llywellyn King of Gwynedd and Powys, and invaded England, sacking Hereford in Oct 1055.
He was reinstated in 1056 when Gruffydd accepted Edward's overlordship. Florence of Worcester records that Ælfgar was appointed to succeed his father in 1057 as Earl of Mercia, the earldom of the East Angles passing to Gyrth, son of Godwin. The Anglo-Saxon Chronicle records that in 1057 he was banished again, but Florence of Worcester states that he forced his restoration in 1058 with the help of Gruffydd and a Norwegian fleet.
His death removed from the scene the only potential challenger to Harold Earl of Wessex. Orderic Vitalis records that “Elfgarus comes” had founded “Coventrense cœnobium” and that “Godiova...comitissa” donated “omnem thesaurum suum” to the church. 1
Ælfgar gained from the exile of Earl Godwin of Wessex and his sons in 1051. He was given the Earldom of East Anglia, which had been that of Harold, son of Godwin. Earl Godwin and King Edward were reconciled the following year, so Harold was restored to his earldom - but not for long. At Easter 1053 Godwin died, so Harold became Earl of Wessex, and the earldom of East Anglia returned to Ælfgar.
Ælfgar seems to have learned from the tactics Godwin used to put pressure on King Edward. When he was himself exiled in 1055, he raised a fleet of 18 ships in Ireland and then turned to Wales, where King Gruffydd agreed to join forces with him against King Edward. Two miles from Hereford, on 24 October, they clashed with the army of the Earl of Herefordshire, Ralph the Timid. The Earl and his men eventually took flight, and Gruyffdd and Ælfgar pursued them, killing and wounding as they went, and enacting savage reprisals on Hereford. They despoiled and burnt the town, killing many of its citizens. King Edward ordered an army mustered and put Earl Harold in charge of it. This was more formidable opposition, and Ælfgar and Gruyffdd fled to South Wales. However the issue was resolved by diplomacy and Earl Ælfgar was reinstated. 2