Thomas "Tommy" Gregson is a NYPD Captain of the 11th precinct. He previously worked at Scotland Yard which is where he met Sherlock Holmes.
Tommy Gregson started working for the NYPD thirty years ago. He was assigned to Scotland Yard a few months after the September 11 attacks to observe their counter-terrorism bureau. Although Sherlock was mostly assigned to homicides, their paths still crossed a few times. Ten years later, When Sherlock moves to New York City where Tommy currently lives and works as Captain of the New York Police Department, he hires him as a consultant detective.
He was married to Cheryl Gregson, and has several adult daughters. One of them is named Hannah and she works as a police officer at the same precinct as her father and wishes to become a captain like him (Rip Off).
When Sherlock is kidnapped, Joan becomes worried when he doesn't answer her messages. Suspecting that he may have relapsed, she tells Tommy that she's a sober companion for recovering drug addicts, and that Sherlock is her client. After Sherlock is found, Tommy tells him that he knew he was in rehabilitation before he hired him to work for the NYPD, and that since his services as a consulting detective hasn't altered, he doesn't see a problem with it.
It is revealed after a break-in in his house that he and his wife are on a trial separation. Cheryl is tired of Tommy's job being prioritized over her, but Tommy thinks the trial separation is just a break for Cheryl and that she'll come back. After realizing why his wife wanted a separation, he lets her know that she deserves better and that he is going to use the separation to figure out how to give it to her.
Tommy physically assaults his daughter’s partner after learning he was abusive with her in the context of a romantic relationship. His daughter, Hannah, is not pleased with way he handled the situation, feeling he has caused talk among her fellow officers. Tommy discusses the situation with Kitty Winter and she helps him understand his daughter’s position, and her desire to keep from appearing as a victim to her colleagues. Tommy eventually agrees to shake the officer's hand in front of the precinct. The officer tells Tommy he is quitting the force and seems scared, Tommy then realizes that Kitty intimated the officer.
Tommy's daughter Hannah asks for Joan's assistance with a case involving a string of robberies. Joan pieces the case together and gives Hannah the information to take to the lead detective. She then discovers that Hannah has chosen to act on the information herself to win a commendation and advance her career as opposed to following proper procedure. Tommy learns of the situation and advises Joan not help Hannah again.
Tommy gets a chance for a promotion. He considers it, even getting Joan to investigate his possible successors, however he ultimately decides he is happy with his current position.
Tommy has a new girlfriend Paige, a former police officer, that was forced to resign. When Joan runs into them at a coffee shop she inadvertently triggers their break-up, Paige had wanted to keep their relationship a secret from Tommy's work colleagues. It is later revealed that the larger reason Paige broke things off was because she was recently diagnosed with Multiple Sclerosis. Tommy wants to be with Paige, even with her health issues. Tommy convinces Paige to resume their relationship.
As a favor to Tommy's girlfriend, Paige, Sherlock investigates her doctor's staff, and finds evidence of wrong doing. However, in doing so he uncovers that Paige is having financial difficulties. Sherlock suggests that Tommy marry Paige so that she may be covered under his insurance, Tommy admits that he loves Paige and wants to marry her, but she isn't keen to do so. Sherlock arranges a meeting between Tommy and Paige after speaking to her about marriage. Apparently he got her to “lower her defenses” and then told Tommy they should get married because Tommy said he wanted it. Sherlock even provided a selection of rings.
In "Henny Penny the Sky Is Falling" the city wishes to recognize the Major Crimes division, and Tommy wants Joan and Sherlock included in the commendation. Sherlock is against this and tries to sabotage Tommy's efforts with his higher ups, while Joan tries to encourage the recommendation. Joan eventually convinces Sherlock to accept the honor.
Every photo of Tommy Gregson on this wiki can be seen here.
Arthur Conan Doyle's Inspector Gregson on Wikipedia, which Elementary's Tommy Gregson is based on.