Harry Bauer is an agent with Cobra.
Cobra is an unofficial organization created by the Five Eyes nations (US, UK, Canada, Australia, and New Zealand) to "take out the trash". As was explained to Bauer, the Director of Cobra, Russell Bertrand, convinced people in high places in those nations to allow and to fund Cobra.
"We are not officially recognized, but we sit uneasily within the gray area of national security, where the executives of the member nations have special powers. We identify targets that we feel should be eliminated, we propose them and, usually, we eliminate them. Sometimes member governments come to us and ask us to take out a particular target. Our criteria for elimination is that the target in question should be truly and unambiguously evil beyond any doubt, they should be a significant threat to other human beings, and must have committed a crime, or be, demonstrably, about to commit a crime, that is truly and unambiguously evil."
To carry out the mission of Cobra, it needs highly trained and capable agents like Harry Bauer to be its assassins. Bauer would take a good deal of convincing to join, largely because while he knew he had the skill and the talent for what Cobra was looking for, he had issues with what Cobra was all about.
Bauer was born and "raised" in New York City. The quotes around raised is because he did most of his raising himself. Being left at an orphanage as a baby, named by the people there, he left the institution as soon as he felt able to take care of himself and spent his teen years living on the streets. It was there that his sense of outrage at the frequent incidents of injustice he routinely saw started eating at him and he started to do something about it. To help him survive this new avocation, he studied tae kwon do, getting a black belt in it, and then becoming good enough in jeet kune do to be an instructor.
When a personal issue pushed him to leave, he left the country and worked his way across the Atlantic on a ship. Once in England, he applied for and got accepted to try out for the Special Air Service (SAS). He discovered that as incredibly difficult as the training was, he relished it and he was good at it.
And the eight years he would go on to serve were the best years of his thus far unhappy life for in the Regiment, he had found the family he never had before. Which is why when his actions fell afoul of Whitehall and he was given the choice of resigning or getting thrown out, he reluctantly chose the former and made his way back to the States.
Being a trained and experienced killer as he had been with the SAS made Bauer a valuable asset (until he wasn't) but that sort of skillset does not translate at all to the civilian life. Unless you want to work for organized crime, like he was doing when a job for the Russian Mob came along. It does, though, make you a candidate for working for the ultra-covert Cobra.
Talking of his leaving New York a decade before, Bauer tells us, "I had left ... a pregnant wife. If she had been my wife I would have stayed."
Replying to Bauer's request for who she was and who she worked for, Cobra bigwig Jane Harris replies, "I don't have to tell you anything or explain anything or abide by any rules or protocols. I don't exist. I am not even here, and never was."