The Oxford Dictionary of National Biography states that Walter de Burgh was the first earl of Ulster, a magnate, and a soldier, and that he was [1]
… the second son of Richard de Burgh (d. 1243), lord of Connacht, and Egidia, daughter of Walter de Lacy, lord of Weobley and Meath. Richard de Burgh died early in 1243 while serving on Henry III's expedition to Poitou. His heir was his eldest son, Richard, who by December 1243 was attached to the king's household. He was granted his inheritance in 1247, and knighted by Henry III at Winchester at Whitsun 1248. He died the following November … At the time of his brother's death Walter de Burgh was in Ireland and still under age. In October 1249 Henry paid his expenses in coming to England at his order, and the next few years saw de Burgh establish connections that were to be significant for his future career. Like Richard, he was attached to the royal household as a king's yeoman (valettus regis); in May 1250 he was granted his brother's lands, though his marriage was reserved to the king. … he was mostly outside Ireland until after the Gascon campaign of 1253–4, on which he served. Also in Gascony was John fitz Geoffrey, the justiciar of Ireland, a key link between the court and the barons whose lands lay chiefly in Ireland. About 1257 de Burgh married John's daughter, Avelina …
Many of his deeds are recorded by the Gaelic Irish annalists, by whom he is often called Mac William Burke, a reference to his grandfather, William de Burgh (d. 1206) …
In July 1263 Walter de Burgh was with the Lord Edward, to whom Henry III had granted Ireland in 1254, during military operations at Bristol. There he received a grant of Ulster, which had been in the king's hand since the death of Hugh de Lacy in 1242, to hold as Lacy had held it. … Walter de Burgh is called earl of Ulster by the annals of Connacht in 1264 (Annala Connacht, 143), and he was addressed as earl by Henry III from 1266. …
Earl Walter died at Galway on 28 July 1271 … His widow died in May 1274 … In addition to his successor, Richard de Burgh (d. 1326), Walter and Avelina had a son named Theobald (d. 1303), and a daughter, Egidia, who married James Stewart, the high steward of Scotland (d. 1309).
[1] Robin Frame, "Burgh, Walter de, first earl of Ulster (d. 1271)," Oxford Dictionary of National Biography (Oxford University Press, 2004, online edition), [Oxford_Dictionary_National_Biography], [OxfordDNB(UM)].