In 2001, Renshaw directed Taboo, a musical with the book by Mark Markham, lyrics by Boy George, and music by Boy George, Kevan Frost, Richie Stevens and John Themis, in London. He work-shopped Zorro, a new musical with the book by Helen Edmundson, lyrics by Stephen Clark and music by the Gipsy Kings and John Cameron, in London, San Francisco, Los Angeles and New York. In 2008, the production went on a UK national tour before opening in the West End. Renshaw later directed Zorro in Paris, Moscow, Tokyo, Amsterdam and Atlanta.
In 2016 he directed the world premier of Carmen La Cubana, billed as "The First Cuban Musical", at Paris’s Théâtre du Châtelet. Carmen La Cubana narrates a gripping love story set against the backdrop of 1950s Cuba, at the dawn of the revolution.