The most common and most likely answer to this crossword clue is the 9 letter word STRUTTING
I've seen this crossword clue in Financial Times
S
T
R
U
T
T
I
N
G
More clues leading to the result STRUTTING
Buddy explains!

The straight part
We know that "Cocky-looking" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cocky-looking = strutting.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 STRUTTING mean?
STRUTTING verb- To swell; protuberate; bulge or spread out.
- (originally said of fowl) To stand or walk stiffly, with the tail erect and spread out.
- To walk proudly or haughtily.
- To cause to swell; enlarge; give more importance to.
- To protrude; cause to bulge.
- To brace or support by a strut or struts; hold in place or strengthen by an upright, diagonal, or transverse support.
- The act of one who struts.