The persona of the Red Hood has been used by both the Joker and Jason Todd, both of which have been referenced in previous Batman: Arkham games - The Jason Todd version of the character was referred to by the Jokers phrase "Didn't I kill you already?" when playing as Robin on the "Jokers Funhouse" map, in Batman: Arkham City's challenge mode, and the Joker version of the character is actually playable in a flashback sequence in Batman: Arkham Origins, when the Joker is being interviewed by Harleen Quinzel.
As the above picture shows, it seems as though the player will be able to play as Jason Todd's version of the Red Hood in a Story mode DLC for the forthcoming Arkham Knight. It looks like, despite the Jokers demise in Arkham City, the clown prince of chaos' influence is still being felt throughout Gotham City!