After qualifying as a veterinarian, he moved his practice to British India, where he became an expert on the camel. He worked there for six years before becoming Camel Specialist for the East Africa Protectorate of the British Empire. He would remain an animal lover and teetotaller throughout his life.
He published numerous articles on the camel and its maladies, the first appearing in "The Journal of Tropical Veterinary Science" in 1909. He had the honour of having a camel parasite named after him; Thelazia leesei.
He joined the Royal Army Veterinary Corps of the British Army at the start of World War I and served on the Western Front and the Middle East. Captain Leese returned to England where he continued his practice, retiring and publishing a book, The One-Humped Camel in Health and in Disease (1928), which would remain a standard work in India for fifty years.
Leese was an antisemite for much of his life, a prejudice reportedly kindled by his disgust for kashrut, a set of laws dictating the correct form for preparing food and slaughtering animals. He developed conspiracy theories relating to a perceived Jewish threat to the British Empire, and became involved with fascist groups, starting in 1924. His anti-semitism was hysterical in its intensity, and he even accused rival fascists of being soft on Jews.
As a member of the British Fascists he was elected a councillor in Stamford, Lincolnshire that year, along with fellow fascist Henry Simpson. In his autobiography, Leese wrote "We were the first constitutionally elected Fascists in England".
By 1928, having become disillusioned with the British Fascists, Leese became a founding member of the Imperial Fascist League. By 1933, he found his own Imperial Fascist League being eclipsed and overtaken by Oswald Mosley and the British Union of Fascists. He greatly resented Mosley and dubbed him a "kosher fascist".
Leese's anti-semitism earned him a prison sentence in 1936 when he was indicted along with fellow IFL member Walter Whitehead on six counts relating to two articles published in the July issue of The Fascist (the IFL newspaper). He was convicted and was jailed for six months in lieu of a fine for causing a public mischief.
Released on conditions in December 1943 because of ill health, Leese again returned to prison in 1947 for six months for his part in aiding escaping members of the Waffen SS.
In 1951, he published his autobiography Out of Step: Events in the Two Lives of an Anti-Jewish Camel Doctor.
After the war, Leese also published his own magazine, Gothic Ripples, which was largely concerned with attacking the Jews. A mentor of the young Colin Jordan, Leese left Jordan his Holland Park house (74 Princedale Road, London W11) upon his death (although his widow retained the use of it as a sanctuary), which, known for a short spell as Arnold Leese House, would become Jordan's base of operations.