Sue starts to party early, imbibing wine with Nick (9)
I believe the answer is:
'sue' is the definition.
(I've seen this before)
'starts to party early imbibing wine with nick' is the wordplay.
'starts to' suggests taking the first letters.
'imbibing' is an insertion indicator.
'wine' becomes 'rose' (rose wine is a kind of wine).
'with' is a charade indicator (letters next to each other).
'nick' becomes 'cut'.
The initial letters of 'party early' is 'pe'.
'pe' enclosing 'rosecut' is 'PROSECUTE'.
(Other definitions for prosecute that I've seen before include "Bring a criminal action against" , "Practise" , "Take legal action" , "Bring before a criminal court" , "Pursue" .)