A warrant is a legal document used by many civilizations when a criminal act is suspected of having been committed. A warrant may be issued by the legal authority of a government for the purposes of conducting investigations into criminal acts, or for the detention of an individual or group.
One of the first people, Lee processed into Sanctuary District A during the early 21st century was a woman, who had an outstanding warrant outside for leaving her baby with the people she worked for. (DS9: "Past Tense, Part II")
T'Pol, acting on a warrant issued by the Vulcan Ministry of Security, pursued and captured several fugitives, killing one in the process. (ENT: "The Seventh")
In 2270 Doctor Leonard McCoy was served a warrant by the Dramians on suspicion of having caused a deadly plague 19 years previously. (TAS: "Albatross")
By 2369, the Klaestron government had issued a warrant for Dax for treason and murder. (DS9: "Dax")