Gillespie was an operations division chief petty officer stationed on board the USS Enterprise-D in the late 24th century.
When the Enterprise was trapped in a Tyken's Rift in 2367, Gillespie spent much time in Ten Forward. He told Chief O'Brien that Kenicki reported seeing a man in an old Starfleet uniform riding the lift near the warp core, only to disappear. O'Brien replied he was surprised that Gillespie believed such nonsense and stated that shades and spirits were not something that a good Starfleet officer would ever take seriously.
Later, under the influence of an alien telepathic transmission, Gillespie got paranoid; he believed that their situation was a test conducted by Captain Picard to determine their reactions. Together with others, he tried to leave Ten Forward (under orders not to leave) and overwhelmed two security guards, when he was stopped by Guinan using a Magus III energy weapon. (TNG: "Night Terrors")