The most common and most likely answer to this crossword clue is the 4 letter word SNOB
I've seen this crossword clue in The Daily Telegraph
S
N
O
B
More clues leading to the result SNOB
- Superior type seems noisome and obviously bourgeois, initially
- Shoemaker, one who behaves condescendingly
- Social climber maybe to get weepy hugging knight
- Representative of pretentious nobility
- Pretentious person has a job at last
- Head of Society and VIP who looks down on the lesser orders?
- High-minded type rejected gifts heartlessly
- Be sorrowful about knight who cares too much for social standing?
- One shows arrogance from heads of state? Not one bit
- Highbrow partners get to the heart of phobia
Buddy explains!

The straight part
We know that "One shows arrogance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one shows arrogance = snob.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 SNOB mean?
SNOB noun- A person who wishes to be seen as a member of the upper classes and who looks down on those perceived to have inferior or unrefined tastes.
- A cobbler or shoemaker.
- A member of the lower classes; a commoner.
- A workman who works for lower wages than his fellows, or who will not join a strike.
- (Cambridge University) A townsman, as opposed to a gownsman.