She is an intelligent, determined, and exacting woman who may offend some people involved in her cases, or coworkers, but she has powerful skills to determine the facts of a crime, compel confessions, and close cases. Thus, she is "a closer".
An expert at interrogations, Brenda has a long history in law enforcement. She worked for the police in Atlanta, where she is born and raised, and later for the U.S. State Department as well as the CIA. She was married at one point to a co-worker in Atlanta, but it ended in divorce.
In the end of The Closer, due to her efforts to capture Phillip Stroh leading her to assault him, Brenda, knowing she will lose her job, leaves the LAPD and gets a new job as Chief at the District Attorney's Office's Bureau of Investigation. While its more administrative, she can still work in the field sometimes. She also has Gabriel transferred there to act as liaison officer for the LAPD.
In season 3 of Major Crimes, Fritz tells the team she's considering a new job in Washington, DC. However, Fritz gets a job as Deputy Chief of the Special Operations Bureau of the LAPD and it is unknown how it affects her choice. She is also unaware that Fritz had a heart attack and now needs a pacemaker with only Michael Tao knowing.