Powerful alien entity like Ares, Apollo, or Hyperion. He is more ethereal in nature and routinely possesses host bodies. He is one of the beings who visited Earth thousands of years ago and seeded the mythology of the Greek gods. After they left Earth, he was eventually imprisoned at the Galactic Core on the planet Pharos. He was imprisoned by an entity named Ramses "The Son of Light" and builder of things. Given his ability to take hosts, he was imprisoned inside a brain dead man named Proteus.
He is the enemy of the being Ares and the Titans like Hyperion. Zeus is the "God" encountered by Kirk and the crew of the USS Enterprise-A. What was not know is that he was not destroyed, as presumed, but took Sybok as a host. ("Star Trek V: The Final Frontier)
Escaping aboard a Bolian vessel that had gone to the Galactic Core, he was eventually "rescued" by crew of the USS Gilbert. He killed the crew and eventually possessed the ship itself.
He, still in Sybok's body, beamed over to the Potemkin. He demanded to be taken to Hyperion so he could destroy the Titan. When the crew refused he forced Warp, Prax, and Arnet to relive their deepest pains and fears. He then took Bom as a host and started wreaking havoc, threatening to destroy the ship if the crew refused to cooperate.
Eventually Zeus abandoned Bom for Sybok's body again, but was then tricked by the blue engineer into being blown out an airlock and the Vulcan's body was then destroyed by phasers. However, the malignant entity fled in the Gilbert.
A few months later he came to Arx Stellaris IV, where the crew happened to have just found out that leader is Ares, another entity like Zeus. He and Ares were mortals enemies and soon began to battle, with the crew caught in the middle.
Unfortunately, Ares revealed that Zeus could not be ultimately killed. That's why he had imprisoned in the first place. Zeus eventually fled from Arx Stellaris. Before leaving to chase after him, Ares told Warp to seek out Ramses - the one who had imprisioned Zeus thousands of years ago - and that he would only answer to the name "Ozymandias."
In "Doomsday" the crew actively sought out Zeus with Ozymandias to imprison him behind the Great Barrier again. Zeus, having already done some battle with Ares and Hyperion, broke through the shields and jumped into his favorite of all hosts - Bom.
Bom/Zeus came to the bridge and wreaked utter havoc. Ares and Hyperion were no match, not to mention the crew that tried to stop him. He jumped from Bom to Arkin, all the while stopping all opposition against him. Eventually he left Arkin and threw Ares and Hyperion through the bridge skylight. He drained Hyperion completely of power, and turned to fighting Ares. However, Ozymandias was able to blast him with energy through the deflector dish - trapping him in the Galatic Core forever. Adding to this punishment, Ares was trapped along with him; the two would go on battling for eternity. The Potemkin had seen the last of Zeus.