Total, say, or just a bit (4)
I believe the answer is:
some
'a bit' is the definition.
(I've seen this in other clues)
'total say' is the wordplay.
'total' becomes 'sum' (synonyms).
'say' indicates a 'sounds like' (homophone) clue.
'sum' sounds like 'SOME'.
'or just' acts as a link.
(Other definitions for some that I've seen before include "An undetermined number" , "Several" , "A little; not a little" , "Hard work" , "Part" .)