Korax was the Klingon executive officer of the IKS Gr'oth, serving under the command of Captain Koloth in 2267.
While drinking in the bar while on shore leave aboard Deep Space K-7, Korax and a number of his crew, traded insults with Montgomery Scott and Pavel Chekov and a number of the crew of the USS Enterprise (NCC-1701) who were also on the station. The insults, stemming from calling Captain James T. Kirk a "Denebian slime devil" to calling the Enterprise a "garbage scowl"; words that eventually ignited an all out brawl between the two crews. (TOS: "The Trouble with Tribbles", DS9: "Trials and Tribble-ations").
Korax would later serve, again, as the executive officer aboard the IKS Devisor, in 2269, Captain Koloth. (TAS: "More Tribbles, More Troubles")