Miss sleep after onset of storm (4)
I believe the answer is:
skip
'miss' is the definition.
(to skip something is to miss it out)
'sleep after onset of storm' is the wordplay.
'sleep' becomes 'kip' (synonyms).
'after' is a charade indicator (letters next to each other).
'onset of' suggests taking the first letters.
The initial letter of 'storm' is 's'.
'kip' after 's' is 'SKIP'.
(Other definitions for skip that I've seen before include "Jump lightly over; refuse container" , "Omit - jump over rope" , "Gambol" , "Omit; fail to attend" , "Miss - waste container" .)