A puppet master was a figurative term used to describe one entity that covertly controlled the actions of another, such as a figurehead.
In 2380 and 2381, the Klingon Captain Dorg was the puppet master behind the Pakled attacks on the Federation. (LD: "wej Duj") Early in 2381, the crew of the USS Titan attempted a covert mission to Karzill IV to uncover who the puppet master was, but were at the time unsuccessful. (LD: "Kayshon, His Eyes Open")