The most common and most likely answer to this crossword clue is the 4 letter word FRAY
I've seen this crossword clue in The Times
F
R
A
Y
More clues leading to the result FRAY
Buddy explains!

The straight part
We know that "fight" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fight = fray.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 FRAY mean?
FRAY verb- To (cause to) unravel; used particularly for the edge of something made of cloth, or the end of a rope.
- To cause exhaustion, wear out (a person's mental strength).
- Frighten; alarm
- To bear the expense of; to defray.
- To rub.
- A fight or argument
- Fright.