Qi'ra was sold by the White Worms to the Crimson Dawn.
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Throughout the film, Qi’ra attempts to protect Han from the truth about the life she's led in the three years since his escape and her arrest on their home planet of Corellia. While he's continued to dream of buying a ship and returning to rescue her, she's been sold to Crimson Dawn, the most ruthless crime syndicate during the Empire’s reign. She works for Dryden Vos (Paul Bettany), and has committed unspeakable crimes on his behalf.
From Star Wars databank,
But Qi’ra was a survivor. She managed to escape Corellia after all, rising in the ranks of the crime syndicate Crimson Dawn to become Dryden Vos’s most-trusted lieutenant.
The brand on her wrist signifies that she has an allegiance towards this gang, not Dryden Vos, which we can see at the end of the film when she leaves Solo and contacts the syndicates real head honcho: the Sith Lord Darth Maul. This is what Darth Maul says,
Bring the ship and come to me on Dathomir and you and I will then decide what to do about the traitor, Beckett, and his accomplices. I'm on my way. Qi'ra, you and I will be working much more closely from now on.