Unlike Burton’s Batman, Nolan didn’t kill off The Joker at the end of The Dark Knight. That means he’s likely hanging out in Arkham. But with Heath Ledger’s death, we won’t be hearing any mention of him in the final movie of the trilogy. IGN found a quote from Nolan where he explains it:
“We’re not addressing the Joker,” Nolan told Empire. “That is something I felt very strongly about in terms of my relationship with Heath [Ledger] and the experience I went through with him on The Dark Knight. I didn’t want to in any way try and account for a real-life tragedy. That seemed inappropriate to me. We just have a new set of characters and a continuation of Bruce Wayne’s story. Not involving the Joker.”
There is an eight-year time jump at some point in The Dark Knight Rises (probably after Bane snaps Batman like a twig), so that would help in not having to mention the Joker.