Sergeant-major has to go up in the murk (4)
I believe the answer is:
smog
'the murk' is the definition.
'sergeant-major has to go up in' is the wordplay.
'sergeant-major' becomes 'sm' (military abbreviation).
'has' is a charade indicator (letters next to each other).
'to go up in' becomes 'og' (I can't explain this - if you can you should believe this answer much more).
'sm'+'og'='SMOG'
(Other definitions for smog that I've seen before include "Polluted haze" , "Pollutant fog" , "Fog and smoke mix" , "Smoky haze" , "Visible air pollution" .)