The most common and most likely answer to this crossword clue is the 6 letter word WASTES
I've seen this crossword clue in The Daily Telegraph
W
A
S
T
E
S
Buddy explains!

The straight part
We know that "deserts" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deserts = wastes.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 WASTES mean?
WASTES noun- Excess of material, useless by-products or damaged, unsaleable products; garbage; rubbish.
- Excrement or urine.
- A waste land; an uninhabited desolate region; a wilderness or desert.
- A place that has been laid waste or destroyed.
- A large tract of uncultivated land.
- The part of the land of a manor (of whatever size) not used for cultivation or grazing, nowadays treated as common land.
- A vast expanse of water.
- A disused mine or part of one.
- The action or progress of wasting; extravagant consumption or ineffectual use.
- Large abundance of something, specifically without it being used.
- Gradual loss or decay.
- A decaying of the body by disease; wasting away.
- Destruction or devastation caused by war or natural disasters; See "to lay waste"
- A cause of action which may be brought by the owner of a future interest in property against the current owner of that property to prevent the current owner from degrading the value or character of the property, either intentionally or through neglect.
- Material derived by mechanical and chemical erosion from the land, carried by streams to the sea.
- To devastate, destroy
- To squander (money or resources) uselessly; to spend (time) idly.
- To kill; to murder.
- To wear away by degrees; to impair gradually; to diminish by constant loss; to use up; to consume; to spend; to wear out.
- Gradually lose weight, weaken, become frail.
- To be diminished; to lose bulk, substance, strength, value etc. gradually.
- To damage, impair, or injure (an estate, etc.) voluntarily, or by allowing the buildings, fences, etc., to fall into decay.