The most common and most likely answer to this crossword clue is the 4 letter word HALE
I've seen this crossword clue in The Daily Telegraph
H
A
L
E
More clues leading to the result HALE
Buddy explains!

The straight part
We know that "Fit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fit = hale.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 HALE mean?
HALE noun- Health, welfare.
- Sound, entire, healthy; robust, not impaired.
- To drag or pull, especially forcibly.