Back-up story accepted by judge (6)
I believe the answer is:
relief
'back-up' is the definition.
(a back-up provides relief cover)
'story accepted by judge' is the wordplay.
'story' becomes 'lie' (story can mean a fabrication).
'accepted by' means one lot of letters goes inside another (inserted letters are accepted).
'judge' becomes 'ref' (referee).
'lie' going within 'ref' is 'RELIEF'.
(Other definitions for relief that I've seen before include "outstanding work" , "Person replacing another on duty" , "Freeing of besieged city" , "Alleviation of anxiety" , "Help or easement" .)