The most common and most likely answer to this crossword clue is the 5 letter word AUDIT
I've seen this crossword clue in The Times
A
U
D
I
T
More clues leading to the result AUDIT
- Praise out of place in review of books
- Check a Buddhist at regular intervals
- Do books acclaim hiding place?
- Do books sound mostly tedious at first?
- Papers turned up in car, briefly — and so do books?
- Gold European concealed from parliament in survey of accounts
- Warm approval is out of place for vetting of books
- A Buddhist regularly missing inspection
- Initially act upon Morse's sound assessment
- Look at account that's initially given after a 1965 crisis
Buddy explains!

The straight part
We know that "vetting of books" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vetting of books = audit.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does AUDIT mean?
AUDIT noun- A judicial examination.
- An examination in general.
- An independent review and examination of records and activities to assess the adequacy of system controls, to ensure compliance with established policies and operational procedures, and to recommend necessary changes in controls, policies, or procedures
- The result of such an examination, or an account as adjusted by auditors; final account.
- Spiritual counseling, which forms the core of Dianetics.
- A general receptacle or receiver.
- An audience; a hearing.
- To examine and adjust (e.g. an account).
- To conduct an independent review and examination of system records and activities in order to test the adequacy and effectiveness of data security and data integrity procedures, to ensure compliance with established policy and operational procedures, and to recommend any necessary changes
- To counsel spiritually.
- To attend an academic class on a not-for-academic-credit basis.