The most common and most likely answer to this crossword clue is the 10 letter word CHOCOHOLIC
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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 = chocoholic.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 CHOCOHOLIC mean?
CHOCOHOLIC noun- Someone who has such a liking for chocolate that they appear to be addicted to it.
- Addicted or seemingly addicted to chocolate; characteristic of a chocoholic.