The most common and most likely answer to this crossword clue is the 4 letter word COIR
C
O
I
R
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The straight part
We know that "Fibre" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fibre = coir.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 COIR mean?
COIR noun- The fibre obtained from the husk of a coconut, used chiefly in making rope, matting and as a peat substitute.