The most common and most likely answer to this crossword clue is the 8 letter word QUARTILE
I've seen this crossword clue in The Guardian
Q
U
A
R
T
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Buddy explains!
The straight part
We know that "A fourth" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a fourth = quartile.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 QUARTILE mean?
QUARTILE noun- Any of the three points that divide an ordered distribution into four parts, each containing a quarter of the population.
- Any one of the four groups so divided.