Some TMNT stuff was always meant for grownups.
Karai was introduced in Teenage Mutant Ninja Turtles Volume 1, during the "City at War" storyline. She came from Japan to New York to unify the warring factions of the Foot Clan that had risen following the death of Oroku Saki. Shredder's Elite Guard forces had been randomly attacking anybody seemingly without reason. Karai offers the Ninja Turtles a deal; if they assist in stopping the Elite, she will give them a peace treaty with the Foot.
The Turtles reluctantly agree to the truce, and fight to the top of her skyscraper, taking out the Elite stationed there. When they reach the top, they witness a group of slain Foot Soldiers, along with the body of a young girl - Karai's aide and daughter. Karai makes Leonardo swear that they will kill all of the Elite Foot in retribution.
Karai then dons the armor of the fallen Shredder, leading a pack of Foot Soldiers. An Elite mistakes her for the real Shredder, and is shocked. Following this is a final confrontation against five Elite Foot. Karai, in the guise of Shredder, demands that they all commit seppuku. Only one weak-willed Elite complied, but the others demanded the identity of The Shredder revealed. After revealing she was not Oroku Saki, Karai threw the helmet at an Elite and a grand battle ensued. When the fight was over, the Turtles and Karai were the only ones left alive, and despite the Turtles' protests that she owed them nothing, she gave her word that the deal would be honored and that she herself would return to Japan to spread her daughter's ashes and begin a journey of atonement.
Karai was not seen again in the comics until Volume 4, in which a band of mysterious warriors from seemingly another dimension had begun giving the Foot trouble. She hires Leonardo as security, and they capture one of the warriors to interrogate. Karai later lies to Leonardo about the Foot possessing books on mystical arts, which Leo can see right through and notes that because Karai is normally an exceptional liar, something was either bothering or manipulating her.
A few weeks later, Karai visits a local high profile nightclub with an entourage of Foot bodyguards and mingles, eventually meeting Casey Jones. Still longing for his wife April O'Neil (presently on a soul-searching pilgrimage), Jones begins dousing one too many drinks and is soon injured in a bar altercation. Karai brings him back to her private condo, where he awakens in nothing but his underwear, remembering nothing of the previous night. He later discovers a humble and noticeably light-hearted Karai knows something of the night before, but is hesitant to tell him. The thread is never picked up again, as the series was canceled.
A series of storylines in Tales of the TMNT, focusing on the Turtles lives in the future, reveal Karai as an elderly woman, still residing in New York, and very much still in control of a ninja faction. Lonely and longing for "the old days", she uses her new baby granddaughter to manipulate one of the Turtles, Raphael, into facing a gauntlet of enemies, whom he slays in self-defense. Raphael is appalled that the once great Foot leader has been reduced to a sadistic and shallow individual and leaves her to her bitterness.