The most common and most likely answer to this crossword clue is the 5 plus 3 letter word OCEAN BED
I've seen this crossword clue in The Daily Telegraph
O
C
E
A
N
B
E
D
More clues leading to the result OCEAN BED
Buddy explains!
The straight part
We know that "Yet it’s not the place for a deep sleep" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case yet it’s not the place for a deep sleep = ocean bed.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.