The most common and most likely answer to this crossword clue is the 9 letter word THUMBS-UP
I've seen this crossword clue in Financial Times
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Buddy explains!

The straight part
We know that "sign of approval" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sign of approval = thumbs-up.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 THUMBS-UP mean?
THUMBS-UP noun- A gesture signifying approval or okay; a thumb pointing up out of a fist.
- An approval or okay.
- To approve with a thumbs-up sign.