Failed to hear the weather (4)
I believe the answer is:
mist
'the weather' is the definition.
(mist is a type of weather)
'failed to hear' is the wordplay.
'failed' becomes 'missed' (missing is a kind of failing).
'to hear' indicates a 'sounds like' (homophone) clue.
'missed' sounds like 'MIST'.
(Other definitions for mist that I've seen before include "low-level cloud" , "Think fog or low cloud" , "Fine spray" , "Slight fog" , "Thin layer of fog" .)