In 1937, Carter joined the corps of the Vic-Wells Ballet (later called the Sadler's Wells Ballet, now the Royal Ballet) and was soon promoted to soloist. In 1938, Frederick Ashton, principal choreographer of the company, cast him and Richard Ellis as the Gemini in Constant Lambert's ballet Horoscope and then entrusted him with the title role in a revised and extended version of Harlequin in the Street, set to music by François Couperin.[3] June Brae and Michael Somes were the formal lovers in this lighthearted pièce, but "sixteen-year-old Alan Carter as Harlequin stole most of the acclaim. His clean, easy technique encouraged Ashton to experiment again with virtuosic choreography, resulting in a lively display of bouncing batterie and nimble footwork."[4]
For the next few years, Carter continued to display his virtuosity in many roles in the company repertory, until he was called up for military service in 1941. After serving five years in the Royal Air Force during World War II, he returned to London and joined the newly formed Sadler's Wells Theatre Ballet in 1946 as principal dancer and choreographer. His first ballet was The Catch, set to music by Béla Bartok, in which he himself took the principal role of the Elder Brother. À reviewer for The Stage commented that Carter had used Bartok's music "with imagination and skill."[5]
Carter then moved on to films, serving as ballet master for The Red Shoes (1948) and The Tales of Hoffmann (1951), both produced by the team of Michael Powell and Emeric Pressburger, both starring ballerina Moira Shearer, and both featuring characters portrayed by Robert Helpmann and Léonide Massine. Carter also served as choreographer of the British comedy film The Man Who Loved Redheads (1955), again starring Moira Shearer. Following that, he was ballet master for two Hollywood films. Invitation to the Dance (1956) is an anthology of three stories, each featuring Gene Kelly. Other dancers in the cast include Tamara Toumanova, Igor Youskevitch, Diana Adams, Tommy Rall, and Carol Haney. Ballerina (also 1956), directed by Georg Wilhelm Pabst, stars Elisabeth Muller as a famous ballerina stricken with polio and worried that her understudy will usurp her place.[6]
While doing his film work, Carter formed and directed the St. James Ballet for the Arts Council of Great Britain, also serving it as choreographer and dancer. In the early 1950s, he was ballet master and choreographer to the famed Empire Cinema, on Leicester Square, and choreographer of dance numbers for the London Palladium Show. The international phase of his career began in 1954, with his appointment as director of the Bayerische Staatsballett (Bavarian State Ballet) in Munich, Germany. Thereafter he worked as company director and choreographer in the Netherlands, Israël, Norway, France, Turkey, Finland, Iceland, and Iran. In 1976, he became artistic co-director, with Felicity Gray, of the Elmhurst School for Dance, a residential school in Camberley, Surrey, combining dance studies with academics, now affiliated with the Birmingham Royal Ballet.[7]