The most common and most likely answer to this crossword clue is the 4 letter word DOZE
I've seen this crossword clue in The Times
D
O
Z
E
More clues leading to the result DOZE
- Forty winks? Just under twelve
- Sleep lightly, being nearly twelve
- Sleep, and rise finally after twelve?
- They say some deer get little sleep
- Practise Buddhism with reduction in sleep
- Take five or twelve, unfinished
- Drop off speaker’s notes
- Twelve shortly take a nap
- Drift in and out of sleep as 12 noon slips away
- Almost 12? Sleep
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 = doze.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 DOZE mean?
DOZE noun- A light, short sleep or nap.
- To sleep lightly or briefly; to nap, snooze.
- To make dull; to stupefy.
- To bulldoze.