Doze, nod off briefly (3)
I believe the answer is:
nap
This clue is a double definition.
'doze' is the first definition.
(I've seen this in another clue)
'nod off briefly' is the second definition.
(I've seen this in another clue)
(Other definitions for nap that I've seen before include "Siesta" , "Raised surface of a fabric and short sleep" , "Take forty winks" , "A brief sleep, forty winks" , "Little sleep" .)