Stewart Stockman qualified (MRCVS) at the Royal (Dick) Veterinary College, Edinburgh, in December 1890 and after study visits to Paris and Brussels was appointed professor of bacteriology and pathology at the Royal Veterinary College in 1892. At the outbreak of the Anglo-Boer War in 1899 he came to South Africa as a civil veterinary surgeon attached to the Army Veterinary Department. During the war he was veterinary officer with the Rhodesian Field Force. After the war he saw service in the Civil Veterinary Department of India (1902-1903), but returned to South Africa in May 1903 to take up the post of principle veterinary officer in the newly established Civil Veterinary Department of the Transvaal Colony.
Although he spent only two years in the Transvaal, Stockman played an important role in establishing an efficient veterinary service in the colony. During 1903-1904, in collaboration with Arnold Theiler*, he investigated east coast fever, which had just been introduced from Mozambique. Their results were reported in their annual reports and in papers in the Journal of Comparative Pathology and Therapeutics (1904, 1905) and the Journal of Tropical and Veterinary Science (1906). Stockman also published articles on swine fever, "Measles in swine and cattle", and east coast fever in the Transvaal Agricultural Journal (1904). In May 1904 he and Theiler represented the Transvaal Colony at the Inter-Colonial Veterinary Conference in Cape Town, where considerable attention was given to the investigation of east coast fever. He became a member of the Transvaal Veterinary Medical Association in 1903, served on its council during 1904/5, and after leaving South Africa was made an honorary associate in 1908.
Stockman returned to England in 1905 and became chief veterinary officer and director of veterinary research in the Ministery of Agriculture and Fisheries in London. Between 1909 and 1913 he was co-author (with J. M'Fadyean) of several papers in the Journal of Comparative Pathology and Therapeutics, in which they reported on their investigation of contagious abortion in cattle. Stockman also at some time published A text-book of meat inspection. From 1905 to his death in 1926 he served on the council of the Royal College of Veterinary Surgeons, for several years as vice-president, and as president in 1923-1924. He was honoured with the J.H. Steel Memorial medal in 1905 and a KCMG (Knight Commander of the Order of St Michael and St George) in 1913.