Between 2000 and 2007, Besley had postdoctoral research appointments at the University of Nottingham, the University of Sussex, and the University of Cambridge. In 2007 Besley was awarded a Royal Society Relocation Fellowship at the University of Nottingham and a Visiting Academic Research Fellowship at the Australian National University, Canberra.
At the University of Nottingham, Besley was appointed to Lecturer in Theoretical and Computational Chemistry in 2011, followed by promotion to Associate Professor in 2014, and to Professor of Theoretical and Computational Chemistry in 2015. Besley is featured in an expert database for Outstanding Female Scientists and Scholars “AcademiaNet: Profiles of Leading Women Scientists”.
Her research includes the development of theoretical and computational methods for the prediction of materials properties; computational modelling of the behaviour, properties and manipulation of nanomaterials; investigations into the electrostatic interactions and self-assembly of materials; gas storage and interactions in porous solids. She has investigated how the electron beams of transmission electron microscopes interact with materials.