The most common and most likely answer to this crossword clue is the 4 letter word MOKE
I've seen this crossword clue in The Daily Telegraph
M
O
K
E
More clues leading to the result MOKE
Buddy explains!

The straight part
We know that "donkey" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case donkey = moke.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 MOKE mean?
MOKE noun- A donkey.
- A mesh of a net, or of anything resembling a net.
- A black person.
- A stupid person; a dolt.
- (theatrical slang) A performer, such as a minstrel, who plays on several musical instruments.