Anne Gillespie Shaw was born in 1904 in Uddingston, Scotland. She attended the independent St Leonard's School in St Andrews, and then Laurel Bank School in Glasgow. She graduated from Edinburgh University in 1927 with a degree in psychology. She also obtained a social science diploma from the same university. She continued her studies in the United States of America at the Bryn Mawr University, Pennsylvania, becoming a research assistant to Dr Lillian Gilbreth. Shaw went on to work at the Gilbreth Motion Study Laboratories at Montclair, New Jersey.

Shaw returned to Britain in 1930, joining the Personnel Department at Metropolitan-Vickers Electrical Co Ltd three years later as a personnel officer. Here she set up a Motion Study Department, the first of its kind in Britain, and took on the role of Chief Supervisor of Women. During her time at Metropolitan-Vickers, Shaw married John H Pirie. Metropolitan-Vickers operated a marriage bar at the time, meaning that women had to leave the company's employment on marriage. Shaw successfully campaigned for the company to remove its marriage bar in 1938.

During the Second World War, Shaw's work in improving the production techniques of the company came to the attention of Sir Stafford Cripps, Minister of Aircraft production. He invited her to join his Ministry’s Production Efficiency Board in 1942, where she organised motion-study training courses for members of the aircraft industry, and developed an organisation of Personnel Management Advisors for factories working for the Ministry.

In 1945, Shaw left Metropolitan-Vickers to form her own company, the Anne Shaw Organisation Limited, which specialised in the application of motion-study in industry and commerce.

Shaw published "The Theory and Practice of Motion Study" in 1945, "The Full Application of Motion Study" in 1950, and "The Purpose and Practice of Motion Study" in 1952. She was appointed as a Commander of the Order of the British Empire (CBE) in 1954 for her services to the field of personnel management.

Anne Gillespie Shaw died in Macclesfield in 1982. In 2017, she was inducted posthumously into the Scottish Engineering Hall of Fame.