The most common and most likely answer to this crossword clue is the 7 plus 3 letter word SHOWING OFF
I've seen this crossword clue in The Guardian
S
H
O
W
I
N
G
O
F
F
Buddy explains!
The straight part
We know that "Ostentatious behaviour/Ostentatious behaviour" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ostentatious behaviour/ostentatious behaviour = showing off.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.