Brought over to make debut, starring in entertaining little piece (4)
I believe the answer is:
stub
'entertaining little piece' is the definition.
'stub' can be an answer for 'piece' (stub is a kind of piece). I'm not sure about the 'entertaining little' bit.
'brought over to make debut starring' is the wordplay.
'brought over' is a reversal indicator.
'to make' becomes 'but' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'debut' says to take the initial letters.
The first letter of 'starring' is 's'.
'but'+'s'='buts'
'buts' backwards is 'STUB'.
'in' is the link.
Can you help me to learn more?
(Other definitions for stub that I've seen before include "Stump, of a cigarette say" , "evidence of smoking, for example" , "Put out" , "Knock (toe); short remnant" , "Tooth remnant" .)