Judge admitting priest in mitigation (6)
I believe the answer is:
relief
'mitigation' is the definition.
(thesaurus)
'judge admitting priest' is the wordplay.
'judge' becomes 'ref'.
'admitting' indicates putting letters inside.
'priest' becomes 'eli' (I've seen this before).
'ref' going around 'eli' is 'RELIEF'.
'in' is the link.
(Other definitions for relief that I've seen before include "Rest - cure" , "Easement of pressure or pain" , "Relaxation following distress" , "Deliverance from siege" , "Lessening or removal of pain" .)