This role will run for a period of four months, to provide continuity for RBC and to ensure that there is experienced leadership in place while they search for a permanent Principal.
Shirley has worked at RBC since 2001, and she succeeds Professor Julian Lloyd Webber, who stepped down last month.
She is internationally known as a musicologist, focusing on French Baroque music, in particular the composer Marc-Antoine Charpentier.
"I am delighted to be stepping into the Interim Principal role at the Conservatoire, with which I have such a long and happy association," Thompson said. "I am looking forward to working with colleagues in RBC, the Faculty of Arts, Design and Media, and the wider University in this new capacity over the coming months."