Eyre was the son of the Very Reverend Giles Eyre, Dean of Killaloe, by Mary Cox, granddaughter of Sir Richard Cox, 1st Baronet, Lord Chancellor of Ireland.
His uncle John Eyre also represented County Galway in the Irish House of Commons.
[1] Eyre returned to the Irish House of Commons for Galway Borough in 1748, a seat he held until 1768.
[2] The latter year he was raised to the Peerage of Ireland as Baron Eyre, of Eyrecourt in the County of Galway.
[4] Through his daughter Mary, he was a grandfather of Eleanor Caulfeild, who married William Howard, 3rd Earl of Wicklow, the former MP for St Johnstown.