Be half-asleep (6)
I believe the answer is:
drowse
'be half-asleep' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for drowse that I've seen before include "feel sleepy" , "Feel dozy" , "Nod" , "Doze, be half asleep" , "Snooze" .)