The most common and most likely answer to this crossword clue is the 13 letter word RHINOPLASTIES
I've seen this crossword clue in Independent
R
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Buddy explains!
The straight part
We know that "They can mitigate the problems of ‘prominent’ fibbers?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they can mitigate the problems of ‘prominent’ fibbers? = rhinoplasties.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 RHINOPLASTIES mean?
RHINOPLASTIES noun- A type of plastic surgery that is used to improve the function (reconstructive surgery) or appearance (cosmetic surgery) of a person's nose.