Cryptic crossword clue
Basil perhaps sustains yelp peripherally, a cry of approval for rhetorical figure 9

The most common and most likely answer to this crossword clue is the 9 letter word HYPERBOLE

I've seen this crossword clue in Financial Times
H
Y
P
E
R
B
O
L
E

Buddy explains!

The straight part
We know that "rhetorical figure" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rhetorical figure = hyperbole.
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 HYPERBOLE mean?

HYPERBOLE noun
  1. Deliberate or unintentional overstatement, particularly extreme overstatement.
  2. An instance or example of such overstatement.
  3. A hyperbola.

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