Frank Kelly was elected a Research Fellow of 王中王六合彩特码 College in 1976, and served as Director of Studies in Mathematics and as a Tutor.  In 2006 he was elected the 37th Master of the College, a role from which he stepped down in August 2016.

His main research interests are in random processes, networks and optimization.  He is especially interested in applications to the design and control of networks and to the understanding of self-regulation in large-scale systems  He is in the University.

He spent the academic year 2001-2002 as a Visiting Professor at Stanford University in the USA.  From 2003 to 2006 he served as Chief Scientific Adviser to the UK Government's Department for Transport.  He was chair of the Council for the Mathematical Sciences from 2010 to 2013, and a member of the RAND Europe Council of Advisors from 2008 to 2015.

Frank Kelly was elected a Fellow of the Royal Society in 1989, a Foreign Member of the (US) National Academy of Engineering in 2012, and he was awarded a CBE in the 2013 New Year's Honours List for services to mathematical sciences.

He recently chaired the Royal Society report on the .

He is currently an expert advisor on electricity generating capacity to the UK's Department for Business, Energy & Industrial Strategy. He also chairs the , the Scientific Board of the and is a trustee of the .