This is an alternate world of KNY, where Tanjiro and Nezuko have cousins, who were attacked by demons a few days before them. The only survivor, Arakie Kamado, the eldest of the siblings, was infected with demon blood. Not like Nezuko, who became a demon, but the demon that attacked them left blood, and it mixed with Arakie's, causing her to become infected. She decided to become a demon slayer but did not train with anyone, she simply developed her own breathing: Demonic Breathing. Arakie can also regenerate or use Kekkijutsu, which is similar to that of her cousin Nezuko.
The story begins at Ubuyashiki's headquarters.
Ubuyashiki: My swordsmen, today I will introduce you to a new hashira who will be at this rank from now on.
All the pillars fell silent, waiting for the girl to enter Arakie enters the room
Ubuyashiki: This is Arakie Kamado, from today onwards, the Demon Pillar of the Demon Slayer Company. I hope you all get along.
The pillars were perplexed. That girl couldn't have been more than 14 years old, or at least she looked that way. Could a girl that young be a pillar...?
(From here on, you follow the story :) )