The crossword solutions for the term 'Narrowly Defeat, with 'OUT'', are 'NOSE' and 'EDGE'. This phrase is often used to describe a situation in which one competitor or team barely wins over another. It implies that the winner was only able to succeed by a small margin, and that the outcome could have easily gone the other way. The words 'NOSE' and 'EDGE' are used to emphasize this idea of a close victory, as they both refer to something thin or small.