The most common and most likely answer to this crossword clue is the 3 letter word YEN
I've seen this crossword clue in The Times
Y
E
N
More clues leading to the result YEN
Buddy explains!

The straight part
We know that "desire" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case desire = yen.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 YEN mean?
YEN noun- The unit of Japanese currency (symbol: ¥) since 1871, divided into 100 sen.
- A coin or note worth one yen.
- A strong desire, urge, or yearning.
- To have a strong desire for.
- Opium.