Big cat is company, a sweet thing — but not small (6)
I believe the answer is:
cougar
'big cat' is the definition.
(I've seen this in another clue)
'company a sweet thing but not small' is the wordplay.
'company' becomes 'co' (abbreviation).
'a sweet thing' becomes 'sugar' (sugar is sweet).
'but not' is a deletion indicator.
'small' becomes 's' (abbreviation - e.g. clothes size).
'sugar' with 's' taken away is 'ugar'.
'co'+'ugar'='COUGAR'
'is' acts as a link.
(Other definitions for cougar that I've seen before include "N American mountain lion, puma" , "North American puma" , "Large American feline" , "Big cat" , "Cat, aka puma" .)