Adam Burke is an agent with the CIA.
More specifically, as we see very clearly in the opening of the first recorded adventure, he is an assassin for the Agency. He has been with that Intelligence department for several years having been 'hand-picked' by recruiters for the CIA while he was part of the Special Reconnaissance Airmen in the U.S. Air Force. He had, we are told in one place, been in the military for well over a decade.
As we encounter him, we learn that he has an ongoing issue with alcohol and from what we can see in several scenes, while Burke is maintaining control, the spirits are gaining ground. Burke is also seen doing a fair amount of fidgeting when stationary: "He had to move his body. Had to do something before darkness consumed him with violent images and rage took over."
This will change over time but it will be a while. His consumption is a result of the memories of some of the things he has seen in his time with the Air Force and the CIA and because of the loss of his beloved son a couple of years before we meet him. That loss has also brought about a temporary separation from his wife, Laura.
Burke works under the direction of a handler named Naomi Watkins, a very capable and tough lady who is more than capable of holding her own against guys like Burke.
Burke is flexible in his work conditions in that he can and does operate on solo missions when needed but he is also quite comfortable working with a small team, especially when it consists of two old friends, Archie 'Archy' Mack and Bart 'Jonesy' Jones, as well as a female operative named Emily Kilpatrick.