The most common and most likely answer to this crossword clue is the 9 letter word APPETITES
I've seen this crossword clue in The Guardian
A
P
P
E
T
I
T
E
S
More clues leading to the result APPETITES
Buddy explains!

The straight part
We know that "Desires" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case desires = appetites.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 APPETITES mean?
APPETITES noun- Desire to eat food or consume drink.
- Any strong desire; an eagerness or longing.
- The desire for some personal gratification, either of the body or of the mind.