The most common and most likely answer to this crossword clue is the 8 letter word SHUT-EYE
I've seen this crossword clue in Financial Times
S
H
U
T
-
E
Y
E
More clues leading to the result SHUT-EYE
- Shot they use as result of good lie?
- Small booth with Observer and Time Out
- Stop reading our mag, Kip!
- Sleep in small shed with view
- Sleep that’s rapid coming upon the old
- Back in embrace of woman, still you soundly sleep
- No boxer enjoys this rest
- Look after son's home and sleep
- Sleep in small shack with vigilance
- Sleep with looker after bar
Buddy explains!

The straight part
We know that "rest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rest = shut-eye.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 SHUT-EYE mean?
SHUT-EYE noun- Sleep.