The Federation department responsible for criminal investigation and policing, seen arresting Leonard McCoy in 2285 and, by the 32nd century, operating as an arm of Starfleet under officers such as Nhan.
Federation Security is the agency that handles police work within the Federation. In Star Trek III: The Search for Spock its officers detain Doctor McCoy in a San Francisco bar while he is trying to charter a ship to the Genesis planet, and hold him until Kirk and Sulu break him out.
By the 32nd century of Star Trek: Discovery the agency appears to have taken over the role once filled by Starfleet Security. Commander Nhan returns in the fourth-season episode Rubicon as a Federation Security officer assigned to oversee the pursuit of Cleveland Booker and Ruon Tarka.
In the fifth season the files on the fugitives Moll and L'ak carry an instruction to contact Federation Security, and its personnel, by now including Romulans from Ni'Var, guard the couple in Erigah.