Narrowly defeat, with "out"
I believe the answer is:
edge
'narrowly defeat with out' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for edge that I've seen before include "Margin, outside limit" , "The part farthest from the middle" , "Creep" , "Guitarist with U2" , "Keenness" .)