Exercise US prosecutor books? He'll still find fault with it (6)
I believe the answer is:
pedant
'he'll still find fault with it' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'exercise us prosecutor books?' is the wordplay.
'exercise' becomes 'pe' (Physical Education).
'us prosecutor' becomes 'DA' (district attorney).
'books?' becomes 'NT' (New Testament).
'pe'+'da'+'nt'='PEDANT'
Can you help me to learn more?
(Other definitions for pedant that I've seen before include "One pays undue attention to the petty details" , "Stickler for minor details" , "Panted like stickler for accuracy" , "Old teacher" , "One is over-concerned with detail" .)