Her heart-shaped face and beautiful physique soon attracted the attention of talent agents. Her film career began with a role in Night into Morning (1951), and she soon co-starred with Peter Lawford in The Hour of 13 (1952). She then appeared in a small role in The Moon is Blue (1953), the film which helped end the system of censorship of Hollywood films which had been in place since 1934. She also embarked on a USO tour the same year to help entertain troops in Korea, followed by a small but heavily publicised role as Richard Carlson's model girlfriend in the science fiction film Riders to the Stars (1954). Another performance was as the female lead opposite actor-director-filmmaker legend Charlie Chaplin in his final comedy to star himself, A King in New York (1957). During the 1960s and 1970s, she appeared mainly in British TV shows and French films.
She was a semi-regular on the instructional series En France (1962) and the leading lady in several episodes of The Saint (1962–69), which starred Roger Moore as Simon Templar. Among her last film credits were two British horror films, The Vampire Lovers (1970) and The Vault of Horror (1973), and she was also a regular in the British sitcom Father, Dear Father (1971–1973). One of her last television roles was in the science fiction serial Star Maidens (1977). Addams retired in the early 1980s, dividing her remaining years between Europe and the United States.
Addams died in 1985 at age 54, reportedly from cancer. She had been a heavy smoker. She was survived by her husband, Jimmy White, and her son.