Harry is effectively one of these as Warden of the Council.
Deconstructed with Sam Vimes in Discworld. Vimes, despite being promoted time after time, is nonetheless an archetypal Cowboy Cop, rejecting the rules if they stop him from doing his job and hunting down criminals - or, as in Night Watch, rejecting the code that has lead to the Watch becoming useless and Ankh-Morpork a police state - and frequently running up against Da Chief in the form of Vetinari (although Vetinari is quite trope-savvy in this case, and appears to willingly take the position of Da Chief in order to nudge Vimes in the right direction). The deconstruction comes because Vimes hates it - he hates that the system does not work, that it forces him to be a Cowboy Cop to get things done and that it keeps trying to push him into chaos when all that is important to him is the law.
Occasionally he resorts to it and the trope is played straight. It is always in circumstances that clearly warrant extreme measures. His rationalization: "It's me doing it." Put it this way; Vimes is a Cowboy Cop who kept getting promoted. He's also very aware that the justification "It's all right to break the rules because it's me doing it" could very easily be the start of a very slippery slope.
A character that is a unmitigated Cowboy Cop, is the wali of Prince Cadram, 71-hour Ahmed. As he says to Vimes (paraphrased): "Your beat is a city you can walk across in half an hour. Mine is a million square miles of barren desert with no company but sword and camel." His rationality is that he must strike first, and swiftly, before the criminal has a chance to. He got his nickname from when he killed a man in the man's own tent after 71 hours, not the 72 mandated by Klatchian hospitality customs, because the man had poisoned a well, and he had testimony and a confession.
When Vimes continues his Cowboy Cop ways in Night Watch, it works so well that Da Chief tries to have him assassinated. Ouch. Da Chief wasn't Vetinari this time- Vimes went back in time many years due to a magical accident and ended up as the Sergeant that trained his younger self. A young Havelock Vetinari actually saved Vimes from assassination at one point. This kind of thing happens on the Discworld all the time; apparently there's nothing that can be done about it....
Sergeant Detritus could be considered a Cowboy Cop as well. In his case, the subversion is that he's a troll officer who usually works the troll beat, and it could be argued that in a culture who regard hitting each other with rocks as a form of conversation, nailing drug-dealers to the wall by their ears is simply maintaining community relations.
The Godfather: Albert Neri was more than a "loose cannon" as a cop. Frustrated at the inability to do anything about the parking violations around the UN building he bashed in the ambassadors' windshields until he was reassigned to Harlem, then he smashed the skull of an unconscious pimp that he had caught molesting a little girl, which got him sent to prison. Fortunately, his father in law knew the Corleones, and Michael was looking for a replacement for Luca Brasi.
In Ragnarok, the first of The Echo Case Files, Navarro, a local police officer, brings a SWAT team along on a Confederate Marshals operation without getting permission from his superior. Except, well, this is a subversion: he's only a maverick because he's acting like a proper police officer in a corrupt department.