The most common and most likely answer to this crossword clue is the 13 letter word NAME-DROPPING
I've seen this crossword clue in The Guardian
N
A
M
E
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D
R
O
P
P
I
N
G
Buddy explains!
The straight part
We know that "pretentious behaviour" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pretentious behaviour = name-dropping.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 NAME-DROPPING mean?
NAME-DROPPING verb- To casually mention a well-known or illustrious person or the titles of their works, often implying familiarity or association, especially in order to impress others, increase one's status, or to appear knowledgeable or fashionable.
- The practice of casually mentioning famous or important people or the titles of their works, subtly implying familiarity or association, in order to impress others.