Go in vain, perhaps, on the quiet (6)
I believe the answer is:
vanish
'go' is the definition.
(I know that vanish is a more specific form of the action elapse)
'vain perhaps on the quiet' is the wordplay.
'perhaps' is an anagram indicator.
'on' says to put letters next to each other.
'the quiet' becomes 'sh' (both can be said to tell someone to be quiet).
'vain' anagrammed gives 'vani'.
'vani'+'sh'='VANISH'
'in' acts as a link.
(Other definitions for vanish that I've seen before include "Become invisible" , "Evanesce" , "Disappear (in a puff of smoke?)" , "make go" , "Go missing" .)