I think one of the reasons we rarely see any sort of Federation law enforcement service is that in a society that has abolished poverty and inequality, there would only rarely even be a
need for police. Much of police work is essentially done to preserve the existing hierarchical social order and in reaction to people committing acts coded as "criminal" because of the various forms of oppression to which they are subjected. In a society like the Federation, where everyone's material, medical, and mental health needs are met, there would rarely ever be a
need for a police force.
In any event, the canonical evidence and some non-canonical evidence has been gathered in this thread. We know from TSFS that there's something called Federation Security (established as having the full name of the Federation Security Agency) which had the authority to place McCoy under arrest in 2285 for attempting to book passage to the Genesis Planet after it had been cordoned off within UFP territory. We know there was some sort of traffic enforcement service that Young James T. Kirk was attempting to evade circa 2245. We know from the novels (non-canon) that there's something called the United Earth Police, and that there are also peace officers on the planet Izar and local municipal police forces in the capital city of Cestus III.
As a supporter of the
police abolition movement, I would speculate that an enlightened society like the Federation would keep these services on an extremely tight leash, and that their operational ethos is fundamentally different from that of modern policing services. I would imagine that there would only very rarely ever be a need for true cops -- I imagine the traffic enforcer we saw in ST09 might not be a "cop" in the modern sense because they may only have authority to regulate vehicular traffic and have no authority to use force except in extreme circumstances.
Re: The Federation Security Agency in the novels. The books have established the following functions for the FSA:
- Foreign intelligence (in rivalry/coordination with Starfleet Intelligence and the Federation Reconnaissance Office [aka, the Federation Intelligence Community])
- Counter-intelligence
- Civilian interstellar traffic enforcement
- Presidential and VIP protection detail
- Federation-level domestic law enforcement
Its foreign intelligence division seems to correspond in duties to the CIA or MI6; its counter-intelligence and domestic law enforcement missions seem comparable to those of the FBI or MI5; its interstellar traffic enforcement mission seems comparable to the U.S. Coast Guard; and its protection division seems comparable to the Secret Service or Scotland Yard Special Branch.