Mouthpiece separate: might player want more than this? (3,4)
I believe the answer is:
bit part
'might player want more than this?' is the definition.
(an actor might want more than just a bit part)
'mouthpiece separate' is the wordplay.
'mouthpiece' becomes 'bit' (I've seen this in another clue).
'separate' becomes 'part' (both can mean to split or break apart).
'bit'+'part'='BIT PART'
(Other definitions for bit part that I've seen before include "'Small role in film or play (3,4)'" , "Tool" , "cameo" , "Small acting role" , "extra work, perhaps" .)