A taxi driver was someone who operated a taxi as their profession.
On Sigma Iotia II in 2268, Spock told James T. Kirk that his abilities as a taxi driver left much to be desired after Kirk had difficulty operating a car on the planet. (TOS: "A Piece of the Action")
Upon nearly colliding with a time traveling Kirk, a taxi driver employed by Cab Co. used a colorful metaphor to criticize him in 1986 San Francisco. (Star Trek IV: The Voyage Home)