Put to sleep, perhaps (4)
I believe the answer is:
bore
'put to sleep perhaps' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for bore that I've seen before include "Drill or be tedious" , "... endured" , "Carried - drill" , "Drill to be tiresome" , "Wearisome person" .)