The most common and most likely answer to this crossword clue is the 6 plus 4 letter word TURKEY COCK
I've seen this crossword clue in The Guardian
T
U
R
K
E
Y
C
O
C
K
Buddy explains!
The straight part
We know that "One struts around" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one struts around = turkey cock.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 TURKEY COCK mean?
TURKEY COCK noun- A male turkey
- (by extension) A pompous or self-important person