Richard Walters Crozier was born at Numurkah, Victoria. At the outbreak of the First World War he was living and working in Culcairn, New South Wales as a farmer. Crozier enlisted in the Australian Imperial Force on 16 January 1915. He was aged 23 at the time and had no prior military experience. He departed Newcastle aboard HMAT Bakara on 22 May 1915. Crozier was assigned to the 6th Australian Light Horse and remained with this unit throughout his service. His younger brother, Private Sydney George Crozier, also served with this unit in the Middle East.

He arrived at Gallipoli on 2 October 1915. He received a minor shrapnel wound to the neck on 25 November 1915 and was sent to Malta to receive medical attention. Crozier re-joined his unit at Maadi, Egypt on 8 February 1916. Richard Crozier was killed in action on 4 August 1916 during the battle of Romani, the last Ottoman offensive against the Suez Canal, and is buried at Kantara War Memorial Cemetery, Egypt.