A career military man, Norman Arthur received his training at Royal Military Academy Sandhurst and became a commissioned officer with the Royal Scots Greys in 1951. Early in his service, he was chosen to represent Great Britain in eventing at the 1960 Rome Olympics, where he failed to finish individually, but placed fourth with the team. His military advancement culminated in the position of General Officer Commanding, Scotland, which he held from 1985 through 1988, and he was also colonel of the Royal Scots Dragoon Guards from 1984 through 1998. Over the course of his career, he was awarded several times, including being made a Commander of the Royal Victorian Order.