A number of ‘gaps’ may be present within public engagement with research – disparity of skills, priorities and knowledge between research staff and engagement practitioners, as well as differences between institutional ambition and departmental reality. Such gaps are often perceived as problems – deficits to be addressed through training and culture change initiatives. The design and delivery of Imperial College London’s Engagement Academy with 12 members of research, teaching and professional services staff sought to explore and work across such gaps. We propose that these areas of disconnect within and across universities may be challenging, but they may also be structurally necessary, and potentially even a source of rich public engagement.