Cryptic crossword clue
Arrogant greeting good worker could eventually deny 4,3,6

The most common and most likely answer to this crossword clue is the 4 plus 3 plus 6 letter word HIGH AND MIGHTY

I've seen this crossword clue in The Guardian
H
I
G
H
A
N
D
M
I
G
H
T
Y

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 = high and mighty.
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.

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