William Gillespie was born in China in 1905, the fourth child and only son of missionary parents. The family returned to Britain in 1915 to further their children's education and settled in Edinburgh. By obtaining scholarships, Gillespie graduated in medicine at the University of Edinburgh in 1929. After short periods as a house physician, he obtained a travelling scholarship to study in Vienna, officially to study psychiatry and neurology but keen to pursue his interest in psychoanalysis, including through an analysis with Edward Hitschmann.
Gillespie returned to London in Dec 1931 and began work with elderly patients at Tooting Bec Hospita. He submitted a psychoanalytically-based thesis on senile dementia for his MD degree and was accepted for training at the British Psychoanalytical Society, entering into analysis with Ella Sharpe. During lectures by John Rickman, he met his first wife, Dr Helen Turover; they married in 1932 and had two children shortly afterwards. In 1937 William became an Associate Member of the British Psychoanalytical Society and passed the examination for the Royal College of Physicians. In the mid-1930s, he also started part-time work at the Maudsley Hospital, with which he was involved until his mandatory retirement at the age of 65. During the Second World War, he worked full-time in the Emergency Service of the Maudsley affiliate at Mill Hill.
In the same period, Gillespie participated in in the Controversial Discussions at the British Psychoanalytical Society. He worked with like-minded colleagues to formalise the running of the Society with a new constitution, which included tenure limits for officers. Sylvia Payne was then elected president of the Society in 1944 and Gillespie became director of the London Clinic of Psychoanalysis. By 1947 he had been elected training secretary and became president of the Society in 1950 - at the age of 45, he was by far the youngest to have been appointed to that position - and he has been credited with helping to develop stability within the Society. He also served on special committees of the Society to testify before the Royal Commission on Capital Punishment (1950) and the Parliamentary Committee on Homosexuality (1954/5), both of which contributed to significant changes in national policy.
From 1953, Gillespie was invited to stand for a vice-presidency of the International Psychoanalytical Association and embarked on twenty consecutive years serving on its central executive. He was elected in 1957 as the eighth president of the IPA and served two terms; in 1961, he was elected again as a vice-president and held this post until 1973 when he declined to run again. Here too, he was recognized as an able administrator and contributed to negotiating a rewritten constitution and by-laws for the Association.
In 1975, on his seventieth birthday, Gillespie was elected to honorary membership of the British Psychoanalytical Society. This was shortly after the death of his wife Helen and a year later he married Sadie Mervis, an analytic colleague. In 1976, he became the second Freud Memorial Professor of Psychoanalysis at University College London, where he gave a series of public lectures on Freud's work and its relationship to other disciplines. In 1991, he was elected by the IPA to a lifetime honorary vice-presidency. He died on 17 July 2001, aged 95.