The most common and most likely answer to this crossword clue is the 3 letter word NAP
I've seen this crossword clue in The Times
N
A
P
More clues leading to the result NAP
- Sleep with back of neck not completely visible
- Censure over card game
- Doze, knocking over cooking vessel
- South leaving card game to sleep
- Down in a pillow? Some
- Little crash … pot kicked over?
- Short rest not awfully peaceful at first
- Be critical of backing tipster’s favourite
- Surface on cloth sends pot wrong way
- Siesta in ocean apartment
Buddy explains!

The straight part
We know that "sleep" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sleep = nap.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 NAP mean?
NAP noun- A short period of sleep, especially one during the day.
- To have a nap; to sleep for a short period of time, especially during the day.
- To be off one's guard.
- A soft or fuzzy surface, generally on fabric or leather.
- The common direction, on some kinds of fabric, of the hairs making up the pile.
- To form or raise a soft or fuzzy surface on (fabric or leather).
- A type of bet in British horse racing, based on the experts' best tips.
- A card game in which players take tricks; properly Napoleon.
- A bid to take five tricks in the card game Napoleon.
- To grab; to nab.
- To cover (something) with a sauce (usually in passive).
- (dialectal, Northern England, Scotland) A cup, bowl.