A lot of fan favourite heroes and villains shown throughout the Arkham games strangely disappeared from continuity sometime before Arkham Knight. Some were given short stories attached to Riddler trophies, some were given subtle nods through easter eggs and others simply fell through the cracks. I thought it would be fun to guess where these characters ended up and what they were doing before and during AK.
Shiva only appeared in Arkham Origins but played a huge part in the Arkhamverse. She was the one to convince Quincy Sharp to reopen Arkham Asylum with his mayoral campaign, and thus started the events which lead to Arkham City. During Origins, Shiva was working for Ra's al Ghul. But, she was nowhere to be found in AC alongside Ra's and Talia, and wasn't present for the League's civil war in AK.
I think its clear she left the League of Assassins. I'd like to say she went after her daughter, Cassandra, but there's little to no evidence Cassandra even exists in this universe. In the comics, Shiva has been known to train or retrain heroes in martial arts including Tim Drake and Batman after Knightfall. It would be interesting if Jason Todd approached Shiva for training as he became the Arkham Knight. That would mean Shiva's involvement and interactions have caused two of the biggest plot points within the games. It would also be cool if Shiva led her own division of the League.
After being cut open from the inside and thrown into the lazarus pit, its likely that Basil Karlo died from his injuries. I'm surprised there isn't more mentioning of this in AK since his death is pretty much Batman's fault, which would add to Bruce's guilt. Since Clayface has 8 different variations in the comics, I find it hard to believe another wouldn't take Karlo's place. Perhaps his remains could have been experimented on or even sold to the highest bidder. Someone like Matt Hagen perhaps. All I know is that the Clayface legacy would have definitely continued. Personally I'd like Sondra Fuller to take the mantle since there's a huge lack in female characters in these games.