The most common and most likely answer to this crossword clue is the 8 letter word BOOTLICK
I've seen this crossword clue in The Times
B
O
O
T
L
I
C
K
Buddy explains!

The straight part
We know that "Fawn" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fawn = bootlick.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 BOOTLICK mean?
BOOTLICK noun- A toady or sycophant.
- To seek favor from by fawning, servile behavior.
- To engage in fawning, servile behavior.