The most common and most likely answer to this crossword clue is the 6 letter word ABBOTS
I've seen this crossword clue in Financial Times
A
B
B
O
T
S
Buddy explains!

The straight part
We know that "monks" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case monks = abbots.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 ABBOTS mean?
ABBOTS noun- The superior or head of an abbey or monastery.
- The pastor and/or administrator of an order, including minor and major orders starting with the minor order of porter.
- A layman who received the abbey's revenues, after the closing of the monasteries.
- (British slang) A brothel-owner's husband or lover.
- (British slang) A ponce; a man employed by a prostitute to find clients, and who may also act as a bodyguard or equivalent to a bouncer.