Harry Bryant is the captain of the Rep-Detect department of the LAPD. His job in the film is to deal with a group of escaped Nexus-6 replicants (who he refers to as "skinjobs") that have landed on Earth. Bryant considers civilians to be of little importance in his job and his philosophy is "you're either a cop or little people".
At the film's start, his top Blade Runner, Dave Holden, has been put in hospital, barely able to breathe. He needs to get Rick Deckard - his best ever Blade Runner, now retired. It seems a little persuasion is required to make Deckard get back on the job, and Bryant sends Gaff out to "arrest" Deckard and bring him to Bryant. While Bryant at first makes attempts to be friendly, their meeting soon boils down to pure business as he briefs Deckard on the replicants that he needs to take down: Leon, Zhora, Pris and Roy Batty.
Bryant and Gaff later meet Deckard near a streetside bar after he retires Zhora. Bryant is more friendly to Deckard, boasting to Gaff that he could learn from him. However, his lack of humanity in regard to Zhora's death and the effect it has Deckard is noticeable, as he jokes about it despite noticing the effect it has on Deckard. He also informs Deckard that he now needs to retire Rachel, who has gone rogue after learning her true replicant identity. He then wishes Deckard good luck and leaves the bar.
In Blade Runner 2: The Edge of Human, Bryant dies from health problems shortly after attending Gaff's funeral. It is revealed that he also removed files on the sixth replicant (a discrepancy fixed in the Master Cut) in a conspiracy between the UN and the LAPD to take down Eldon Tyrell/Rosen's business. Deckard meets Bryant in his office and Bryant is a video image of himself, claiming to be in the hospital with an infection. Deckard realizes that the image is a persynth (an image simulation of Bryant based off of his personality and behavoir) and later learns that Eldon's niece, Sarah Tyrell, killed Bryant because she was the real one behind the conspiracy, and Bryant was innocent.