Cryptic crossword clue
Arrogant school bowler, perhaps 4,3

The most common and most likely answer to this crossword clue is the 4 plus 3 letter word HIGH HAT

I've seen this crossword clue in The Times
H
I
G
H
H
A
T

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The straight part
We know that "Arrogant" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case arrogant = high hat.
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 HIGH HAT mean?

HIGH HAT noun
  1. A person claiming to be superior.
HIGH HAT verb
  1. To snub or treat condescendingly.
HIGH HAT adjective
  1. Disdainful; haughty

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