The most common and most likely answer to this crossword clue is the 4 letter word PIXY
I've seen this crossword clue in The Times
P
I
X
Y
Buddy explains!

The straight part
We know that "Fairy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fairy = pixy.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 PIXY mean?
PIXY noun- (fantasy literature, fairy tales) A playful sprite or elflike or fairy-like creature.
- A cute, petite woman with short hair.
- An upper-atmospheric optical phenomenon associated with thunderstorms, a short-lasting pinpoint of light on the surface of convective domes that produces a gnome.