An expert sport shooter, Barnett represented Ireland in the contest for the Elcho Shield on 37 occasions, and twice made the record score. He was one of twelve competitors for the United Kingdom of Great Britain and Ireland in the 1908 Summer Olympics He finished fourth in the 1000 yard free rifle competition. A member of the council of the National Rifle Association of the United Kingdom, he was the captain of the winning team in the Lords vs Commons shooting team at Bisley in 1921–28.