Carefully examine old vicar about spoils from robbery (8)
I believe the answer is:
overhaul
'carefully examine' is the definition.
(to overhaul something is to examine or redesign it)
'old vicar about spoils from robbery' is the wordplay.
'old' becomes 'o' (abbreviation as in OT - Old Testament).
'vicar' becomes 'rev' (short for reverend).
'about' says the letters should be written in reverse.
'spoils from robbery' becomes 'haul' (haul can mean the proceeds from a robbery).
'rev' in reverse letter order is 'ver'.
'o'+'ver'+'haul'='OVERHAUL'
(Other definitions for overhaul that I've seen before include "'Repair, renovate (8)'" , "Inspect and repair" , "Examine and set in order" , "Examine and make any necessary repairs" , "Repair fully and renew" .)