He was born at Coghlanstown, County Kildare, son of Sir Richard FitzEustace, who served briefly as Lord Chancellor of Ireland, and Katherine Preston, widow of William Lawless and of Christopher Holywood of Artane, Dublin.
Like his father, he was High Sheriff of Kildare in 1456, and he was one of the original members of the Brotherhood of Saint George, a short-lived military guild charged with the defence of the Pale.
At his death in 1486 he was one of the largest landowners in Kildare (despite having been imprisoned for debt in the 1450s)[3] An Act of the Irish Parliament of 1472 conferred the office of Lord Chancellor of Ireland on Robert FitzEustace and John Tapton jointly.
[6] Robert had at least seven surviving children: his eldest son and heir Sir Maurice FitzEustace, James, Richard, Oliver, John, Anne and Margaret.
Maurice married his cousin Joan FitzEustace, daughter of Lord Portlester and widow of Richard Plunkett, 2nd Baron of Dunsany.