Passes out: asleep and beginning to snore (7)
I believe the answer is:
elapses
'passes' is the definition.
(I know this)
'out asleep and beginning to snore' is the wordplay.
'out' indicates an anagram.
'and' says to put letters next to each other.
'beginning to' says to take the initial letters.
The initial letter of 'snore' is 's'.
'asleep' is an anagram of 'elapse'.
'elapse'+'s'='ELAPSES'
(Other definitions for elapses that I've seen before include "Passes (in time)" , "Slips away" .)