Remaining sleep, perhaps (4)
I believe the answer is:
rest
'sleep perhaps' is the definition.
(sleeping is a kind of resting)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for rest that I've seen before include "Repose - remainder" , "Take it easy, have a break" , "Balance" , "What's left over" , "Calm" .)