During her first posting in Gotham City, Essen had an affair with a young married cop called James Gordon. The two reunited much later and eventually married.
Sarah was actually first created by Frank Miller during his The Dark Knight Returns mini-series where she is mentioned several times by an aged James Gordon but never seen (apart from in silhouette near the ending).
Her first credited appearance however is in Batman #405 during Batman: Year One, again written by Miller and drawn by David Mazzucchelli.
Although she was created with blonde hair, later artists/colorists sometimes colored her as a redhead.
Major Story Arcs
During Batman: Year One, Detective Sarah Essen is partnered with then Lt. James Gordon who at the time was married to the pregnant Barbara Gordon Sr. When the two reluctantly break off the relationship, corrupt police commissioner Loeb receives photo evidence of the affair and attempts to use it to blackmail Gordon who confesses to his wife before Loeb gets the chance. Sarah moves away to New York soon after these events.
Sarah returns to Gotham years later in Batman #458 having been married to a cop in New York who was killed on the job. Gordon, long since divorced from Barbara, strikes up the relationship again and eventually proposes. The marriage occurs in Legends of the Dark Knight Annual #2.
In the mid-90's stories, Jim Gordon is demoted, and eventually retires from the GCPD due to poor relations with then Mayor Armand Krol. Sarah assumes the position of Police Commissioner but dislikes working along side Batman and Robin and is eventually fired by Krol anyway. When new Mayor Grange comes to power, she is hired as a liaison between the GCPD and the Mayor's office and Gordon returns to the role of Police Commissioner.
No Man's Land and Death
During the final act of the lengthy No Man's Land saga, the Joker kidnapps a large amount of small infants and brings them to the basement of the GCPD building. Sarah is the first one to find him and manages to place him at gun-point but the Joker tosses one of the babies into the air causing Essen to drop her weapon to catch the baby. Cruelly, the Joker shoots her in the head leaving her to die in the basement surrounded by small children. Although the Joker surrenders himself over, Gordon, out of anger, refrains from killing him but instead shoots him in the leg.
Note: In Scott Snyder's Detective Comics #875, flashbacks indicate Sarah had married Gordon much earlier when he was still a lieutenant and was around for Barbara Gordon's teenage years. It is unclear if this was a retcon or a mistake.
Earth-31 (Frank Miller's Dark Knight Universe)
Sarah is mentioned in both The Dark Knight Returns and All-Star Batman and Robin the Boy Wonder which also shares continuity with Batman: Year One.
Batman: Year One
Sarah appears in the DC Animated Original adaptation of Batman: Year One straight-to-DVD movie where she is voiced by Katee Sackhoff.
Batman: The Dark Knight Returns
Grey DeLisle voices Sarah in the animated adaptation of The Dark Knight Returns. She has a much more expanded role than in the original comic.
An older Sarah Essen played by Zabryna Guevara appears in the Fox TV prequel series Gotham. She is the police captain and Hispanic-American and initially is portrayed as jaded by the politics of Gotham's corrupt bureaucracy, standing in the way of an idealistic young James Gordon. As the series progresses, she warms to James and starts to take a more active role in stopping crime in the city.
An Easter-egg in the video game Batman: Arkham City reveals that "Sarah" is password set up by Gordon for his police squad.