Big Eater: Frequently seen snacking on various foods. It's even lampshaded by Natalie and Matt's constant teasing and when Alesha is savvy enough to bring him a pastry to bribe him into doing some research for her.
Cartwright Curse/Dead Partner: And how—his backstory includes a partner who was killed, Matt's the one who accidentally reminds him of this, eerily Foreshadowing his own fate, and DI Wes Leyton (not his partner, but clearly a good enough friend for both of these tropes to apply) is gunned down at the beginning of the episode "Hard Stop"
Disappeared Dad: Much like his US counterpart, he has a rocky relationship with both of his daughters thanks to his alcoholism and his two failed marriages (which are themselves due to his drinking problem).
Drowning My Sorrows / Off The Wagon: Comes very close to being played straight—note the scene in Matt's now deserted apartment where he stares at the beer bottles for what seems like an eternity—but is ultimately averted in "Survivor's Guilt" with the help of his new partner, Sam. Comes even closer in "Hard Stop", where he actually goes so far as to buy a bottle of vodka before coming to his senses and walking out of the store without it.
Heroic BSOD: Suffers this after Matt is killed. It really doesn't help that the whole thing happened right in front of him and that he's already been through this. Has another one after Wes is killed too
Like a Son to Me: Thinks this way about Matt, obvious even before the latter is killed and stated outright when he talks with the mother of his killer—"The police officer who died? His name was Matthew Devlin and he was like. . .MY son." Not surprising, considering how he screwed up with his actual children, thanks to his drinking problem.
Playing Against Type: Walsh is a well-known comedic actor and game show host who has been thoroughly impressive as Brooks.
Abusive Parents: Strongly implied—his contempt for a child abuser—"I know people like you", his feelings about victimized children in general, his empathy with an abused kid—"I've been that kid, Ronnie", and with a young woman who refers to her father as a "bastard"—"Are we related then, do you think?", but neither the extent nor specific perpetrator is ever made clear.
Berserk Button: Several—child abuse, established in the episode "Unloved", Alesha Phillips, established in Alesha, and Ronnie Brooks, established in Honor Bound.
(As he and Ronnie arrest Dr. Merrick, Alesha's rapist)
Merrick (yelps in pain as Matt cuffs him): "You're hurting me!"
Fair Cop/Mr. Fanservice/Pretty Boy: And how, to the point where numerous people have reacted to his good looks, ranging from come-ons and compliments to sarcastic put-downs—even the man suspected of being behind his murder (he isn't) refers to him as "Pretty Boy Cop".
Hidden Badass: At least every other episode he runs down, disarms and disables a suspect, usually while being amazingly polite.
Innocent Blue Eyes: Of the "heroic" variety. To the point where they're the last we see of him.
Kindhearted Cat Lover: Alesha is delighted to learn he has a cat in the episode "Deals", and Ronnie is seen caring for it (and commiserating with it) in "Survivor's Guilt".
Officer O'Hara: He reveals his heritage while trying to gain the trust of a young prostitute he's interrogating and in another episode states that he was given a lot of grief about it during his rookie years—"they called me "Mick" for the first six months because my family are Irish." Though it isn't clear if he's explicitly from Ireland and emigrated to England or if he merely has Irish ancestry but was born in England (like his portrayer).
Raised Catholic: Mentions having lit a candle for a murder victim, "Once a Catholic. . .", but he's also clearly disillusioned with his faith—in the episode "Confession", he states that he hasn't been in a confessional in over 20 years, and the events of that episode offer a pretty strong indication of why this has happened.
Rape as Backstory: By proxy. In "Confession", we learn that two of his childhood friends were molested by their neighborhood priest, but it is left ambiguous as to whether Matt was a victim as well. He denies it throughout the episode, but at the end, admits that he's repressed things so much that he's genuinely uncertain as to what, if anything, happened to him.
Disappeared Dad: And is not looking for Ronnie to replace him. He is also apparently and unwillingly this to his own son, only getting to see him once a month.
Expy: Mike Logan and Ed Green, as far as his temper and poor impulse control go. His behavior in the first two Season 7 episodes displayed some of Ronnie's lesser traits as well—a drinking problem, fragile relationship with his child.
Suspiciously Similar Substitute: Subverted. Despite some obvious similarities with his predecessor—young, good-looking, absent (and possibly abusive) father, there were some equally obvious differences—Matt's temper was generally limited to certain issues, whereas Sam appeared to have a short fuse about everything. Matt also clearly cherished the surrogate father he had in Ronnie. Sam seemed to resent Ronnie's attempts at being this—despite generally getting along, the two simply did not have the rapport that Matt and Ronnie did.
We Hardly Knew Ye: Lasted only two series and disappeared without any explanation, just as he was getting interesting.
DS Joe Hawkins
But Not Too Black: He's taunted about his light skin by a dark-skinned suspect, who alternates between seeming jealous—insinuating that he's had an easier time because of it—or being contemptuous—calling him a "mongrel". The second snipe triggers his Berserk Button.
Iron Lady: Despite her obvious grief and anger, she waits until she's alone in her office with the blinds drawn to cry over Matt's death.
Mama Bear: Is fiercely defensive of her subordinates, to the point where criticizing or harming them (Alesha's assault, Matt's death) is essentially a Berserk Button for her, even as them screwing up provokes a reaction much like that of a disappointed/angry parent.
Put on a Bus: Her absence in Season 7 is explained as her taking a leave of absence to care for her ill mother.
The Bus Came Back: She resurfaces in the 4th episode of Series 8, but technically not as a cop, but rather as the daughter of their prime suspect.
Chekhov's Skill: His previous experience as a defense attorney saves his bacon when he's charged with "perverting the course of justice".
Determinator: His reluctance to give a case up or use any means necessary to win is legendary, and actually comes back to bite him in the ass in his last episode: he gets arrested for perverting the course of justice after some evidence that would have exonerated a murder suspect six years previously was found to have gone missing. The same episode says that his conviction rate is ninety three percent.
Put on a Bus: Although acquitted of charges of perverting the course of justice, he still feels ultimately responsible for the Miscarriage of Justice that occurred—an innocent man went to prison, while a guilty man went free and killed several more victims—and decides to resign from the CPS. He has yet to resurface, but it's entirely possible that he could.
What the Hell, Hero?? His "win at all costs" method of handling a case has led him to do some borderline reprehensible things, all of which tend to have the same theme:
In "Paradise" he takes advantage of his friendship with another lawyer, jeopardizing the man's career, in order to garner necessary information. Upon finding out what he's done, the other lawyer gives him a blistering "The Reason You Suck" Speech and rebuffs James' attempts to make amends (one of the few times he was genuinely sorry for the problems that he'd caused), saying, "I don't want to be your collateral damage anymore."
In "Anonymous", humiliates Matt Devlin in court over an error made during the investigation, accusing him of being both dishonest and incompetent (despite knowing full well that he's neither), discrediting not only his testimony, but possibly his tenure as a detective. When Alesha blasts him for this, he dismisses it as "collateral damage."
"Skeletons". Similarly embarrasses an ex-lover over their past relationship and declares that her sole reason for testifying against him is to get back at him for dumping her. Alesha blasts him for this as well, asking if the woman's reputation was, of course, "collateral damage."
The Casanova: Much like James Steel, he seems to have bedded or flirted with nearly half the female lawyers in London.
Expy: Jack McCoy, even moreso than his predecessor
She doesn't like sexist putdowns either, or people trying to play the race card to garner her sympathy for a cop killer—especially since said cop was her friend and died saving her life.
Broken Bird: And how. Raped by her doctor, loses her friend/mentor before they get a chance to explore their feelings for each other, and another friend is killed saving her life before they can explore their feelings for each other. Unlike most examples of this trope, she appears to have come out of each tragedy stronger than before.
Everyone's Baby Sister: As seen in the episode "Alesha", she also serves as a Berserk Button for everyone in the group—infuriated by what's happened to her, they go all out to bring her rapist to justice. And note that James can barely stand to watch the video of her rape, while Matt can't bring himself to watch it at all.
Iron Lady DI Chandler: "I'd like to cut off his dick with a rusty hacksaw and ram it down his throat!"
Expy: No one in particular, just the "young, pretty, female assistant DA" that's been a standard of the original ever since Paul Robinette departed, though her youth and initial inexperience seem very reminiscent of Claire Kincaid, and she even shows a few flashes of Robinette himself (the abovementioned scene where she bristles at a defense lawyer's race-baiting, plus their race of course).
Idiot Ball: In "Alesha", where she tries to entrap a doctor who touched her inappropriately and gets raped.
Heroic Sacrifice: An Alternate Character Interpretation of the above. She essentially jumped on a grenade, knowing something bad would happen, in order to get justice for all of Merrick's other victims, and knowing he would never pay for her. Indeed, when Matt asks why she went back after he'd already assaulted her, she admits that she wasn't expecting him to rape her, but states, "Someone had to stop him. At least now we can lock the bastard up."
Put on a Bus: In the season 7 premiere, it's mentioned that she was transferred to a senior crown prosecutor position in another office. This narrowly averts a literal Bus Crash, as she would have been a passenger on the ill-fated train otherwise.
Twofer Token Minority: Is black and female. But even though she's the only non-white member of the main cast, it's hard to really call her a "token", given that London's incredible diversity is well represented among the supporting players.
Idiot Ball: Chats with an opposing attorney about the tactics Jake is likely to use, then acts shocked when (a) the woman undermines their strategy by preparing her witness, and (b) Jake and Henry read her the riot act for what she's done.
Chekhov's Skill: Like James, was a defense attorney for a while. Despite nearly two decades having passed since then, he does an excellent, if ultimately unsuccessful job of representing an old friend on a manslaughter charge.
December-December Romance: In the episode "Denial", it's strongly implied that he and the current victim had a relationship back in their younger days, and their present-day conversation indicates that the feelings are still there.