Big cheese possibly glum about nothing (5)
I believe the answer is:
mogul
'big cheese' is the definition.
(thesaurus)
'possibly glum about nothing' is the wordplay.
'possibly' is an anagram indicator.
'about' is an insertion indicator.
'nothing' becomes 'o' (O resembles 0).
'glum' anagrammed gives 'mgul'.
'mgul' going around 'o' is 'MOGUL'.
(Other definitions for mogul that I've seen before include "Mound of hard snow on ski-slope" , "bigwig" , "Mr Big?" , "big shot" , "Important person; snow mound on a ski slope" .)