Weaken in the face of a defeat (4)
I believe the answer is:
fade
'weaken' is the definition.
(fading is a kind of weakening)
'in the face of a defeat' is the wordplay.
'in' indicates a hidden word.
'FADE' can be found hidden inside 'face of a defeat'.
(Other definitions for fade that I've seen before include "Grow dimmer" , "flag" , "Dwindle" , "Bleach or decline" , "Lose colour gradually" .)