The most common and most likely answer to this crossword clue is the 3 plus 3 letter word HIT OUT
I've seen this crossword clue in The Guardian
H
I
T
O
U
T
Buddy explains!

The straight part
We know that "Castigate" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case castigate = hit out.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 HIT OUT mean?
HIT OUT noun- A match or session, particularly for practice.
- A penalty shot, awarded when the ball is deemed to have been sent out of play deliberately.
- A fast gallop.
- An instance of knocking the ball out of a ruck contest.