There is a Star Trek episode where Kirk is forced to watch as Spock and McCoy fight as gladiators against Roman guards. There aren't any Klingons involved, but it does feature Roman clothing. There is another episode where alien brains want Kirk, Ohura and Checkov to fight as gladiators on their planet for the rest of their lives. There is a third episode in which Spock and Kirk are forced to fight in front of Vulcans as part of a Vulcan trial-by-combat marriage ceremony. Their is also a fourth episode in Voyager which features a gladiatorial combat but in a sci-fi arena that looks like the set of "Who Wants to be a Millionaire." Those are the only references I could find, but let's just say that this idea has seen its fair share of screen time on Star Trek.

References: https://en.wikipedia.org/wiki/Bread_and_Circuses_%28Star_Tre... https://en.wikipedia.org/wiki/The_Gamesters_of_Triskelion https://en.wikipedia.org/wiki/Amok_Time http://en.memory-alpha.org/wiki/Tsunkatse_%28episode%29