Gillespie appeared in a string of popular British television series, mostly in the 1960s to 1980s. Credits include The Saint, The Avengers, Doomwatch, The Sweeney, The New Avengers, Survivors, Warship, The Professionals, Mary's Wife, I Woke Up One Morning, Return of the Saint, Bonjour La Classe and Secret Army. More recently, Robert has appeared in New Tricks, with Likely Lads' co-star James Bolam, as well as Jimmy McGovern's Broken, alongside Sean Bean.