Arthur Goule qualified at the Royal Veterinary College, London, as a member of the Royal College of Veterinary Surgeons (MRCVS) in 1871. He worked for some time at Melbourne Veterinary College, Australia, before coming to South African during the Anglo-Boer War (1899-1902) as a civil veterinary surgeon attached to the Army Veterinary Department. He was awarded both the King's and the Queen's medals for his war service.
In December 1905 Goule joined the Natal Civil Service and from June 1906 was stationed at Allerton Veterinary Laboratory near Pietermaritzburg as professional veterinary assistant to the government veterinary bacteriologist, H. Watkins-Pitchford*. He was transferred to the field as district veterinary surgeon at Eshowe in 1909 and in 1912 moved to Pietermaritzburg. In 1916, during World War I, he volunteered for service with the Royal Army Veterinary Corps and did duty in France. On his return to South Africa in September 1918 he was lost at sea when the Galway Castle was torpedoed. His wife Kate Goule had died the previous year.
Goule was a member of the Natal Veterinary Medical Association from the year of its formation in 1909.