The latest episode of Titans has revealed the existence of Roy "Speedy" Harper (and, presumably, his mentor Green Arrow, AKA Oliver Queen) in the reality of the popular DC Universe series. It is unclear, however, if either character will be making an appearance on the show sometime in season 2 as no formal announcements have been made regarding the casting of either character.
The name of Roy Harper is well-known to fans of superhero-themed television. One version of Roy (played by Colton Haynes) joined the cast of Arrow halfway through its first season. This Roy Harper was based on the New 52 version of the character, being a former petty thug who attempted to find redemption aiding Oliver Queen's quest to save their city. The animated series Young Justice had two versions of Roy Harper - the original Speedy, who lost his arm and adopted the Arsenal codename after procuring a cybernetic replacement full of tools and weapons and a clone created by Lex Luthor, who later adopted the name Will Harper after assuming the Red Arrow codename.
Donna Troy drops Roy Harper's name early on in Titans' season 2, episode 2, "Rose." During a stakeout, she credits Roy with giving her a tip that was meant to lead her and Kory Anders to the supervillain Shimmer. Later, once Shimmer is in custody, Donna leaves Kory alone to take a phone call privately. We see from the camera's quick focus on Donna's phone that the call is from Roy Harper.
Neither Oliver Queen nor Green Arrow get a mention, but where there's smoke there's fire, and it's highly unlikely that Roy Harper would have a history with a bunch of other superhero sidekicks without having been a sidekick himself, meaning Green Arrow is likely also one of the not yet specified members of the Justice League in this universe.
First appearing in More Fun Comics #73 in November 1941, Oliver Queen and Roy Harper are one of the surprisingly rare examples of a superhero and his young sidekick who were introduced concurrently during the Golden Age of Comics. The two fought crime together as Green Arrow and Speedy until 1971 and the "Snowbirds Don't Fly" storyline in Green Lantern/Green Arrow, which revealed that Roy had started experimenting with heroin in his mentor's absence (something that actually feels appropriate in Titans' darker tone where Hawk is also a recovering addict). Roy later cleaned up his act, without Oliver's help, and built a new life for himself as a special DEA agent, who also fought crime under the codename Arsenal.
Based on what little we see in this episode of Titans, it seems that this world's version of Roy Harper may have found a similar niche for himself, working for some organization that has advanced intelligence on supervillain movements. He may even have graduated into the Justice League, like his counterparts in the comics and Young Justice. It's also possible that, like in the modern Titans comics, Roy Harper and Donna Troy may have some kind of romantic history. It is unclear, however, if this version of Roy Harper is still holding a grudge against Green Arrow or if the two partners have reconciled, as they eventually did in the comics.