The New Sydney police bureau was the police force in the Sappora system, centrally located on the planet New Sydney. Their jurisdiction included Sappora VII.
After Miles O'Brien disappeared on New Sydney in 2375, Yanas Tigan called in several favors from them. The bureau had heard of a Starfleet Intelligence operative being on the planet and later found O'Brien being beaten up by several Nausicaans. Lieutenant Fuchida later took him to the Tigan's home on Sappora VII.
After it was revealed that Norvo Tigan was responsible for the murder of Morica Bilby, he was arrested by the bureau. (DS9: "Prodigal Daughter")
The name of the police force was not mentioned in dialogue, but is taken from the script.