Esteve-Coll was the first woman director of a national arts collection when she was appointed as director of the Victoria and Albert Museum in 1987, succeeding Sir Roy Strong. She resigned in 1994, mid-way through her second term as director, to take up the Vice-Chancellorship of the University of East Anglia. Dr. Alan Borg succeeded her as its new director, taking the post on 1 October 1995.
Esteve-Coll served as Vice-Chancellor of the University of East Anglia from 1995–97, but was forced to step down after being diagnosed with multiple sclerosis. She said at the time: "It is with real sadness and disappointment that I must acknowledge that I am not able to lead the university into the 21st century." She served as Chancellor of University of Lincoln for seven years, as well as being a Trustee of the Sainsbury Institute for the Study of Japanese Arts and Cultures since its foundation in 2000.
Esteve-Coll received the Order of the Rising Sun, Gold Rays with Neck Ribbon in November 2005 in recognition of her "outstanding contribution to the promotion of Japanese culture and studies to British people". In November 2008, she was presented with an honorary doctorate of arts and the title chancellor emerita during her farewell ceremony at Lincoln Cathedral.