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]
(..) I keep asking and no one wants to tell me. We can't tell you. Only the fire can tell you. What do you see? Logs burning. Keep looking. What do you see? Ice. A wall of ice. The Wall. (..)2017 TvShow: Game of Thrones Title: Dragonstone Season: 7 Episode 1
(..) you were soundly defeated. Come to mention it, weren't you the one who started that rebellion by sailing to Casterly Rock and burning the Lannister fleet? You certainly caught us there. Very smart move on your part. Of course, we all made it to the Iron Islands anyway. I was there. (..)2017 TvShow: Game of Thrones Title: Dragonstone Season: 7 Episode 1