Pass by when asleep, possibly (6)
I believe the answer is:
elapse
'pass by' is the definition.
(to elapse is to run out or pass by)
'asleep possibly' is the wordplay.
'possibly' is an anagram indicator.
'asleep' anagrammed gives 'ELAPSE'.
'when' acts as a link.
(Other definitions for elapse that I've seen before include "Tick by" , "Go past" , "(Of time) go by" , "Passing" , "Of time, pass by - please" .)