The most common and most likely answer to this crossword clue is the 4 letter word BLOW
I've seen this crossword clue in The Guardian
B
L
O
W
More clues leading to the result BLOW
- Very detailed autobiography of English baroque composer?
- Huge birthday dinner? Do this to candles!
- Setback: British crestfallen
- Punch black and blue
- Disappointment felt after this, for character on the radio?
- Drug left in London area
- Fan of Wales at first supports Bale with love
- After opening of bottle, down coke in New York
- As hurricane may be described in every detail?
- Possible description of commentary — in boxing?
Buddy explains!

The straight part
We know that "Fan" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fan = blow.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 BLOW mean?
BLOW noun- A strong wind.
- A chance to catch one’s breath.
- Cocaine.
- Cannabis.
- (US Chicago Regional) Heroin.
- To produce an air current.
- To propel by an air current.
- To be propelled by an air current.
- To create or shape by blowing; as in to blow bubbles, to blow glass.
- To force a current of air upon with the mouth, or by other means.
- To clear of contents by forcing air through.
- To cause to make sound by blowing, as a musical instrument.
- To make a sound as the result of being blown.
- (of a cetacean) To exhale visibly through the spout the seawater which it has taken in while feeding.
- To explode.
- (with "up" or with prep phrase headed by "to") To cause to explode, shatter, or be utterly destroyed.
- To cause sudden destruction of.
- To suddenly fail destructively.
- (used to express displeasure or frustration) Damn.
- To be very undesirable. (See also suck.)
- To recklessly squander.
- To fellate; to perform oral sex on (usually a man)
- To leave, especially suddenly or in a hurry.
- To make flyblown, to defile, especially with fly eggs.
- To spread by report; to publish; to disclose.
- To inflate, as with pride; to puff up.
- To breathe hard or quick; to pant; to puff.
- To put out of breath; to cause to blow from fatigue.
- To talk loudly; to boast; to storm.
- To sing.
- To leave the Church of Scientology in an unauthorized manner.
- Blue.
- The act of striking or hitting.
- A sudden or forcible act or effort; an assault.
- A damaging occurrence.
- A mass or display of flowers; a yield.
- A display of anything brilliant or bright.
- A bloom, state of flowering.
- To blossom; to cause to bloom or blossom.