The most common and most likely answer to this crossword clue is the 7 letter word HAUGHTY
I've seen this crossword clue in The Daily Telegraph
H
A
U
G
H
T
Y
More clues leading to the result HAUGHTY
Buddy explains!

The straight part
We know that "Proud" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case proud = haughty.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 HAUGHTY mean?
HAUGHTY adjective- Conveying in demeanour the assumption of superiority; disdainful, supercilious.