From the beginning it's obvious that this guy wouldn't last long. The Three Kingdoms story is mostly about the struggle between Cao Cao's force, Liu Bei's force, and Sun Ce/Quan's force. Rulers like Gongsun Zan have little chance to compete. Nevertheless, he lasts about the same time as Lu Bu in The Ravages of Time (which is pretty damn long).
Gongsun Zan is initially shown as one of the leaders of the Guangdong Alliance against Dong Zhuo, but Yuan Fang betrays him and other leaders. In fact, Yuan Shao even pursues Gongsun Zan and tries to kill him to get rid of the thorn. This is because Gongsun Zan's domain lies in the north, and it's pretty close to Yuan Shao's northern domain as well. Yuan Shao nearly gets to destroy Gongsun Zan, but Liaoyuan Huo comes along and ruins the Yuan plan. Kidnapping Xiao Meng was not a good idea. And that's where Huo gets his Zhao Yun name, but this post isn't suppose to be about Zhao Yun. Liu Bei and the rest of the Peach Brothers come along and save Gongsun Zan's ass when Liu Bei successfully persuades Yuan Shao to leave.
The next time that Gongsun Zan appears, he is at the mercy of Yuan Fang. He kills his family, and then he commits suicide. He dies just like that. In The Ravages of Time, I think he is used as a way to showcase the extraordinary abilities of the Yuan clan. But yeah, this guy doesn't get much screentime and doesn't get enough characterization either.
(I know I got lazy and recycled these from Yuan Fang so don't ask me for more)