His grandson the 3rd Baronet died childless in 1872, and was succeeded by his younger brother.
The family seat was Glenstal Abbey, near Murroe, County Limerick.
They sold Glenstal and left Ireland in the 1920s, a move largely prompted by the killing of Winifred Barrington, the 5th Baronet's daughter, in an ambush during the Irish War of Independence.
As of 2025, the baronetage is marked dormant on the Official Roll.
[3] The heir apparent is the present holder's son Patrick Benjamin Barrington (b.1988).