Having caught, be quick to discipline (7)
I believe the answer is:
'to discipline' is the definition.
(I've seen this in another clue)
'having caught be quick' is the wordplay.
I cannot really see how this works, but
'caught' could be 'c' (cricket abbreviation) and 'c' is found in the answer.
'be quick' could be 'hasten' (I've seen this before) and 'hasten' is located in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for chasten that I've seen before include "Subdue the pride of, discipline" , "Moderate" , "Subdue - a stench (anag)" , "Censure severely" , "Suppress" .)