The police are individuals empowered by a government to enforce the law.
On Damiano, the Iaron police, with the assistance of the USS Enterprise-D, provide security for Governor Ra'ch B'ullhy. (TNG - Perchance to Dream comics: "To Take Arms Against a Sea of Troubles", "By a Sleep to Say We End", "In the Sleep of Death, What Dreams May Come", "Enterprises of Great Pitch and Moment")
On Ferenginar, the police were considered a collection of whip-wielding thugs who did not know how to solve crimes but did know how to take bribes and beat up people. (DS9 novel: Ferenginar: Satisfaction is Not Guaranteed)
On Nukolee, the police investigated the unrest that had broken out over the planet, but without success. (TOS comic: "A World Gone Mad")
On Tezwa, the military served as the police until USS Enterprise-E security chief Christine Vale began helping to train civilian peacekeeping forces. (TNG - A Time to... novels: A Time to Kill, A Time to Heal)