The Exobiology Council was a Federation agency responsible for authorizing exobiology missions.
In 2347, the council granted permission to Magnus Hansen and his wife Erin to investigate the yet-unknown species called the Borg. (VOY: "The Raven")
Additional duties of this agency, from the Star Trek Encyclopedia, 4th ed., vol. 1, p. 263 included oversight of exobiologists and for advising the Federation on matters pertaining to the biology of life-forms.