That’s part of a long quest line, I’ll quickly sum it up but it spoils most of the game.
First, make your way to New Ark City by leaving the abandoned town. Once in the slums, if you’re strong enough, you can anger one of the local crime lords henchmen. They will then take you to his lair where he offers you to retrieve his slave, who happens to be Cassie.
Afterwards you go back to Cassie and talk to her. I don’t think you actually have an option to betray her, but either way when you next leave and return she’ll be gone. Going back to the crime lords lair you’ll find out his henchmen followed you and kidnapped her.
You then have to start a long quest of befriending various named characters across New Ark City, both in the slums and the central level, and together you’ll forge a plan to break her out. It’s possible to try at pretty much any point, but each additional character will either help you or give you information you need to make the breakout much easier.
Once you defeat the crime lord and get Cassie home safely you’ve gained her trust. It takes quite some time to do tho, so don’t focus on her too much and just enjoy the game. Saving her will come naturally as you progress through the game.