Ariadne first shows up as the Dominion of Chesed during a Dominion meeting in Volume 3, where she joins the discussion about the White Queen threat. She's later brought into the action at Netzach by Yuri Sagakure, arriving alongside Maya Yukishiro and Ouka Miyafuji to stop Kurumi from advancing to Tiphereth—via a Texas Hold'em game, naturally.
She's got this perpetually sleepy look going on, and her Astral Dress actually plays into that, designed to let her sleep anywhere without a care. But Rinemu Kirari hints that the drowsy act is just a cover; there's more going on underneath.
Despite the perpetual exhaustion vibe, Ariadne's legitimately one of the strongest Dominions in a fight—impressive enough that Haruka Kagarike has jokingly suggested handing Gevurah over to her. On top of that, Yuri Sagakure's vouched for her skills as a gambler too, which explains why she was the right pick for that card game showdown.
Content compiled by AnimeList.moe from publicly available sources.