Clarke embraced the role that was once thrust upon him, and 12 years later, he has followed in Street's footsteps again to become Council president, the second-most-powerful man in city government.
Clarke might have been an accidental politician, but his ambition and skill have been quite purposeful.
He is low-key, with a self-effacing smile and an athlete's stride that belie his political prowess and age - he'll be 60 in September. Colleagues say he has quietly risen because of his competence, his mastering of the minutiae of governing, and his ability to build coalitions.
"This is what he does. He works, and he works very hard," said Leigh Whitaker, his former chief legislative aide. "He's not a guy who hangs out. He keeps a very low profile because that's just who he is."
No doubt, Clarke won't be found drinking and cavorting at the Palm after work. And he admits to being reluctant to talk about his personal life.
He never married. He is ultra-proud of his one child, Nicole Bright, whom he helped raise to become a doctor.
Though he's not the type to feature his daughter on his campaign literature, he bristles at the "ridiculous" suggestion that he's excessively private or inscrutable. Catch him in his district, he said, and you'll see that "I can be live and in living color, trust me."
"But," he added, "my position is, people who get stuff done tend not to be the people who do a lot of talking."
And Clarke has a lot of stuff he wants to get done.
Last week, at his first Council meeting as president, Clarke began rolling out his agenda, based on the idea that the city must raise money without raising taxes. Among other measures, he's advocating the sale of public assets and advertising space on public property.
He has other notions that would part with long-standing Council tradition.