Robson Brown joined the faculty at the University of Bristol in 1997 after earning her PhD.^[1] She was elected into a Phyllis and Eileen Gibbs Travelling Research Fellowships.^[2] In her early years at Bristol, she developed the UK's first tomography laboratory within a forensic or physical anthropology department.^[3] From 2005 until 2010, Robson Brown was a founding member of the Human Tissue Authority. In 2005, she was a co-chair of HTA's Import and export working group and Public display working group, as well as a lay member in HTA's Authority.^[4]

During the 2011–12 academic term Robson Brown worked alongside geologist Nicholas Minter and biologist Nigel Franks to examine how nest architecture is influenced by factors both social and environmental.^[5] The next academic term, Robson Brown earned a University Research Fellowship.^[6] The 2015–16 academic year resulted in Robson Brown collaborating with the Radiocarbon Accelerator Unit at the University of Oxford to examine six mortuary chests within Winchester Cathedral.^[7] She was later the recipient of Bristol's 2016/17 Engagement Award for her research project Skeletons: Our Buried Bones, in collaboration with Bristol Museums.^[8]

She was appointed Director of the Jean Golding Institute in August 2017.^[1] With her appointment, Robson Brown earned one of four APEX awards from the Royal Society to research how bones respond to stress.^[9] The next year, she was named Turing University Lead after Bristol joined the Alan Turing Institute.^[10] In 2019, Robson Brown and Heidi Dawson-Hobbis found that remains left behind in Winchester Cathedral belonged to 23 Anglo-Saxon kings and queens, rather than 11 people that was originally thought.^[11] That year also brought about a collaboration between the Jean Golding Institute and Strathmore University Business School in Kenya.^[12] She was also co-director of the Human Spaceflight Capitalisation Office in Harwell.^[13]