She was 'burning for' a chance to prove herself. [=she wanted very much to get a chance to prove herself]
('humorous') “We were talking about you last night.” “That explains why I 'felt my ears burning'.”
She was 'burning with' anger at his rudeness. [=she was very angry because of his rudeness]
(..) delivering the prisoner back to Ysmault? No. You have your sector to attend to, I have mine. Then until we see one another again, my friend. - Keep the light burning. - Always. Set us free and we will serve you as you serve your blue-skinned owners. DEMONIC FACE: Paradise is right here. (..)2011 Green Lantern: Emerald Knights