Judge accepts story in mitigation (6)
I believe the answer is:
relief
'mitigation' is the definition.
(thesaurus)
'judge accepts story' is the wordplay.
'judge' becomes 'ref'.
'accepts' indicates putting letters inside.
'story' becomes 'lie' (I've seen this before).
'ref' enclosing 'lie' is 'RELIEF'.
'in' is the link.
(Other definitions for relief that I've seen before include "Easement from pain or stress" , "Comfort; easing" , "Alleviation - charity - raised decoration" , "That's a load off my mind" , "Break" .)