In the Joker movies, Jim has short brown hair and has a mustache. In other DCEU material, he is portrayed by J.K. Simmons, but in the Joker trilogy, his younger self is portrayed by David Harbour. David Harbour is aged forward ten years or so, so he looks like he could age into J.K. Simmons in five to ten years.
Jim Gordon is a police officer in the GCPD in the homicide branch. He discovered Batman on the GCPD roof and Gordon began giving him tips on crime most nights. He tipped Batman about a drug lord, Jack Monteleone, who goes by the name Candyman. After Batman and Robin defeated Candyman and his associates, Gordon and other police officers came to arrest Candyman. While his partner, Harvey Bullock, was interrogating Candyman on why he sold most of his supply of Acetone- a main chemical in Candyman's drugs- to a "Mr. J.'. Gordon interrupted when on the news, a school bus full of explosives- Acetone- crashed into an elementary school, killing most of the occupants. Most of the police left to catch the suspect and when they did Gordon and Harvey interrogated him.