Krax was the son of Zek, the Ferengi Grand Nagus. He accompanied his father to Deep Space 9 to discuss expanding their business into the Gamma Quadrant. Krax was shocked however when Zek showered Quark with compliments and then announced that he was standing down and making Quark the new Nagus. Shortly after, Zek apparently died.
Since Krax would still become nagus if Quark died, he entered into a conspiracy with Quark's brother Rom, who would similarly inherit the bar if Quark died. Together, they set up a locator bomb that homed in on Quark's pheromones, but the assassination attempt failed when Quark moved at the last minute. They later attempted something more direct: Tricking Quark into entering an airlock by pretending a ship was waiting there to take him to the Gamma Quadrant for negotiations. They then attempted to flush him out into space, but were foiled by the arrival of Odo with the real Zek, who had appointed Quark his successor and faked his death to see how Krax would react. Zek was unimpressed with Krax's clumsy attempt to seize power, telling him he should have accumulated it discreetly from the shadows while keeping Quark as a figurehead.
Krax was not seen again in the series even though Zek reappeared several times. He accompanied Zek to the station in the early novel The Big Game. In the short story "Satisfaction is Not Guaranteed", Krax is working for Rom, now the Grand Nagus. He is part of a conspiracy led by Brunt designed to depose Rom, but actually tricks the conspiracy into playing their hand early with an easily disproved claim that Rom has broken his marriage contract with his first wife.