Cryptic crossword clue
Leave out label initially as an act of snobbery 4-4

The most common and most likely answer to this crossword clue is the 9 letter word NAME-DROP

I've seen this crossword clue in Financial Times
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Buddy explains!

The straight part
We know that "an act of snobbery" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case an act of snobbery = name-drop.
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-DROP mean?

NAME-DROP verb
  1. 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.

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