CIA to try resolving crime (8)
I believe the answer is:
atrocity
'crime' is the definition.
(I have seen 'monstrous crime' mean 'atrocity' so perhaps 'crime' could also mean 'atrocity')
'cia to try resolving' is the wordplay.
'resolving' is an anagram indicator.
'cia'+'to'+'try'='ciatotry'
'ciatotry' is an anagram of 'ATROCITY'.
(Other definitions for atrocity that I've seen before include "'Barbarity, heinous act (8)'" , "Cruel deed" , "Heinous deed" , "Frightful act of citatory kind" , "Outrage" .)