The most common and most likely answer to this crossword clue is the 5 letter word NEGEV
I've seen this crossword clue in The Guardian
N
E
G
E
V
More clues leading to the result NEGEV
- In north-east, for example, start of virtual desert
- Barren ME region some have generously backed
- Barren territory some have gently sent up
- Edible plants raised by Nile’s banks in arid area
- Never ever green, even vaguely? That’s primarily desert
- Semi-desert, say, occupying half of Nevada
- Somewhat unresponsive, gentleman recovered in desert
- Not all move gently backwards to desert
- Origins of geological events seen in Nevada desert region
- Part of Israel‘s green space? On the contrary
Buddy explains!

The straight part
We know that "desert" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case desert = negev.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.