Kay Hamilton is an agent with the Callahan Group.
This private sector enterprise is described as a "shadowy quasi-governmental agency" which says a lot about it while not giving that much away. It is shadowy in that very few people know about it which is how its founder, Thomas Callahan, wants it. It is an agency in that it provides a particular service, 'typically one that involves organizing transactions between two other parties' - in this case it is often the U.S. government requesting the service. It is quasi-governmental in that it is not officially a part of the legitimate authorities but it can certainly call upon its resources easily enough.
Callahan likes to tell new recruits the story of how his Group got started, how he was an assistant to the National Security Council when he was picked by then President George W. Bush to start an unoffical organization to do things Congress should not know about and how he now reports directly to the President's "man" to get orders and to deliver reports. He enjoys relaying it because it is fun to say. It is also not the least bit true. As the series moves, it becomes clear that several high ranking officials in the "real" intelligence community have started the Group and chosen Callahan to run it and that they provide the funding and give the orders, not the President. Much more than that is not yet clear.
Hamilton is at the start of the series not a member of the Group; she had not idea it existed nor would she have cared. She was a dedicated DEA agent with a proven track record for doing whatever it took to get the job done and she was good at it. She was also in charge of a team of agents in southern California and she was most assuredly not good at that. Hamilton is determined to do what is needed and no one, not the bad guys or her team or anyone else had been get in the way because though she did not have the mass for it, she had the force of a steamroller and the willingness to use it. Abrasive is a good word to describe her. So is a five-letter word beginning with 'b'.
She is not a bad person by any means - she just wants to do her work. It is her life and except for the occasional fling that is far more physical than emotional, that is all she has. As the series progresses she will begin to change as her life changes around her but at the beginning, she is highly effective and highly unpleasant. Then when her estranged daughter is put into imminent danger she has to act and that action costs her her job but gives her something better.
Unemployed, she is told at the beginning of the second adventure about the Callahan Group and her life changes even more, as does she.