He has links to Hsin Jaoming and is suspected of masterminding several major counterfeiting operations in Liberty City and around the world.
Along with Wu "Kenny" Lee and Chan Jaoming, he is a contender for the spot as Hsin Jaoming's successor. Both him and Chan were falsely accused of being the FIB informant who was ratting out the Triads (only for it to be revealed to be Kenny), and they were both killed by Huang Lee on Hsin's orders.
He is an extremely arrogant, bloodthirsty triad boss who thinks he has everything to become Hsin's successor. Zhou also owns a bar called the Ming Inn in Broker and an unnamed club in the East Island City district of Dukes.
Zhou Ming drives a white Bobcat as seen in the missions Stealing the Show, Flatliner and Driven to Destruction. He also has a Triad variant Hellenbach, as seen in all of the missions he gives from his clubhouse, in Cash and Burn and in the cutscene for the mission So Near, Yet Sonar.
His name was very likely based on the Chinese dynasties Zhou and Ming.
Suspiciously, a Chinese character in Driver: Parallel Lines exists, named Zhou Ming. Both games are set in an equivalent of New York, and Zhou Ming also appears as a boss for many missions in Driver: Parallel Lines.