Zoology was a branch of biology which involved the study of animals and non-sentient lifeforms, typically conducted by specialized scientist known as a zoologist.
In order to repopulate the surface of Talos IV, in 2254, the Talosians offered their zoological gardens to Christopher Pike, so to help him reclaim the planet's surface with a variety of plant life. (TOS: "The Cage", "The Menagerie, Part II")
While considering the ramifications of hunting down and killing the Mother Horta, in 2267, which Spock deemed as a potential "crime against science," Captain James T. Kirk reminded him that their "mission is to protect this colony, and to get the pergium moving again. This is not a zoological expedition." (TOS: "The Devil in the Dark")
Jadzia Dax had an academic degree, with Premier Distinction, in the subject of zoology. (DS9: "Dax")
Sebarr was a zoologist that worked with Keiko O'Brien during an agrobiology expedition in the Janitza Mountains on Bajor in 2371. (DS9: "Fascination")
A scene cut from "True Q" would have established that Amanda Rogers had been considering a career in zoology. However, this was just one in a series of extremely fleeting ambitions.