Alan Trosper is a former agent with The Firm.
It is clearly stated in the author's foreword of the first book that "there is no element of American intelligence that much resembles 'The Firm'." For this reason, and because there is nothing in the books that suggest otherwise, like references to Langley or the Agency or the CIA directly, it must be assumed that The Firm is yet another covert intelligence bureau in the U.S. community. By inference, it is likely that the agency answered directly to the President.
When Trosper was let go from the Firm several years before the series starts, he tried not to become bitter. The President had told the Controller, as the head of the department was known, to clean house and start fresh. The Controller at the time was a relatively new man to The Firm replacing the founder who had recently passed away. This new man was not well known to the agents and, therefore, blamed for more ills than he might have otherwise since the word from the President was to clean house and reduce costs. Trosper was but one of many given their walking papers with little thanks and no references.
As the series opens, Trosper is enjoying .a solitary life selling high-priced boats to rich people, doing alright for himself, and not anxious at all for the old life, or so he thought. When given a chance to get back into action, though, he hardly hesitated beyond a few token "why should I come back?" questions, showing his true desires.
As the series progresses, he meets someone special and starts a family, showing growth as he continues his career for a while before ending it on his own terms. Of course, just because you quit doesn't mean you're out.