I am confused about the new "Twila-Katherine Price" card.

You can see the card here!

As far as I know, Characters, when commiting to a story, get exhausted. How ca you use her ability then, if she has to be exhausted when commited to a story? Does this card require some combo to be used?

There are a couple of ways you can make use of Ms. Price.

The easiest is to win the Arcane struggle with her at a story and ready her. Then use her action during the action phase after the icon resolutions as characters are still at the story during this action phase.

Also there some cards in the new AP that allow characters to commit to stories without exhausting.

After commiting to a story, there are Action windows, so you could take Actions to ready her and then use her.

Maybe a nice Restless and Wary should help ???

Yup, this card was made with Arcane in mind, and rewarding 'arcane' effects.

Arcanedidn't have that big a link with 'magical abilities' ingame, and now it has

she will be great with rotting way.