Go to sleep, with "out" (4)
I believe the answer is:
conk
'go to sleep with out' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for conk that I've seen before include "(Slang) nose - head" , "Nose, head (sl.)" , "Hooter" , "Punch" , "Blow" .)