Bryan Mills is a former CIA agent.
I almost put down that he was a hostage rescue expert because he most certainly is highly trained and experienced in finding and freeing kidnapped and abducted people but he does not actually earn a living doing that, at least not always.
This are really two versions of Bryan Mills presented to the viewer.
The first one we meet is an elder Mills. He has put his time in with the Agency and chosen to retire. He could still be with that department of the government or he could be making very good money putting his talents on the civilian market but has chosen not to for the same reason he retired in the first place.
Mills had been married to a woman he still loves, Lenore, and they had a child together both dote on, Kim. Mills' work and frequent and prolonged absences due to his job cost him the marriage and Lenore eventually married someone else. Regretting not being there for his daughter and wanting a chance of reconciliation with her, Mills left the CIA and got a safe, sedate job near her.
That might have been the end of the story except for the kidnapping of Kim and the determined efforts of Mills to get her back. However, the violent actions needed to do that will create some nasty enemies which will return for revenge.
Mills will need to show over again how dangerous he is and how good he can be at rescuing people who have been taken.
The second one we meet is the much younger Mills. This is a former Special Forces operative who has a run-in with a powerful drug cartel leader which will cost the life of Mills' sister and forge his determination to get vengeance for her and to bring that leader to justice.
Mills will be shown that doing it alone is suicide and that there was a team of hostage rescue personnel working for government that had a spot he would fit in wonderfully.
Initially, Mills will demonstrate that he is very good at his newly found career but also rash and impetuous and thus prone to making mistakes. It will be a period of learning and maturing through the occasional failure and through successes that were not as good as they should have been.
Eventually that team will fall into disfavor and Mills will join with another operative and a computer hack to work again with Christina Hart, the woman who had run the first team only to see it broken up. Mills will show that he is even better than he was but he is still prone to brash actions.