Drummond Leslie has had a career in university management and governance. He was on the staff of the committee of Vice-Chancellors and Principals of the Universities of the United Kingdom (now Universities UK) holding six consecutive appointments covering virtually all aspects of university activities, and culminating in the post of Head of Administration. Subsequently he was Secretary to the Centre for Commercial Law Studies at Queen Mary, University of London, and Company Secretary of the Higher Education Staff Development Agency, the then National Training Organisation for higher education in the UK.
Educated at the City of London School and the School of Slavonic and East European Studies, University of London, Drummond was awarded first and higher degrees in Russian Language and Literature, studying French as a subsidiary subject at Birkbeck. He was President of his College students' union, and the first sabbatical President of the University of London Union 1967–1968. He was awarded Life Membership of the University of London Union.
He has served in a non-salaried capacity as a member of the governing bodies of five Colleges of the University including University College London; the Institute of Education; Heythrop College; and Birkbeck. He was Vice-Chairman of Heythrop and was made a Fellow of the College in 2006. He was an independent Governor of Birkbeck 2000–2011. He served on the governing body of the University continuously for 27 years and held the elected post of Chairman of Convocation of the University.
Drummond Leslie's interests outside the university sector include classical ballet and contemporary dance, classical and pop music, and railways. Drummond is a Trustee of the Royal Ballet Benevolent Fund and chairs its finance and investments committee, he is a Trustee of the Cecchetti Society Trust, the Cyril Beaumont Scholarship Trust and the University’s Convocation Trust.
He was a Governor of Sadler’s Wells Foundation 1980–1995, as well as a Director of Sadler’s Wells Trust and Sadler’s Wells Theatre Appeal Fund. He was Chairman of the Council of the Friends of Sadler's Wells for 10 years, and subsequently a Vice-President. In 1967, he was admitted as a Freeman of the City of London. He was elected a Fellow of the Royal Society of Arts in 1982 and served until 2007.