Richard was born in County Mayo, Ireland, in 1838, and he moved to Buffalo, New York after emigrating to the United States. He enlisted in the US Army around 1872 and was assigned to Company A of the 1st US Cavalry. By the time Richard deployed to the Arizona Territory, he was a First Sergeant and it was his actions on the 23rd of May 1872, that would earn him the Medal of Honor. The citation reads:

Conspicuous gallantry in a charge upon the Tonto Apaches.

Richard received the Medal of Honor on the 12th of April 1875, and soon after was discharged from the Army. He moved to Washington DC, where he retired and on the 20th of March 1898, Richard Barrett died at the age of 60. He is buried in the US Soldiers’ and Airmen’s Home National Cemetery, in Washington DC: Section K-6765.