The most common and most likely answer to this crossword clue is the 5 letter word PUSHY
I've seen this crossword clue in Financial Times
P
U
S
H
Y
More clues leading to the result PUSHY
- Turned up lacking confidence? Hardly!
- Arrogant sort turns up to bowl
- Forward returned up pitch
- Quietly blocking agreement being upheld, applying pressure
- Backed up attempt, being assertive
- Having overturned drink, discontented hubby is aggressively forceful
- Aggressive, but the opposite when backup goes missing
Buddy explains!

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 = pushy.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 PUSHY mean?
PUSHY adjective- Aggressively ambitious; overly assertive, bold or determined.