Writing by Nick, Elizabeth and Sue (9)
I believe the answer is:
prosecute
'sue' is the definition.
(I've seen this before)
'writing by nick elizabeth' is the wordplay.
'writing' becomes 'prose' (I've seen this in another clue).
'by nick elizabeth' becomes 'cute' (I am not sure about this - if you are sure you should believe this answer much more).
'prose'+'cute'='PROSECUTE'
'and' acts as a link.
Can you help me to learn more?
(Other definitions for prosecute that I've seen before include "Carry out assessment" , "Represent the Crown in court" , "Sue" , "Bring a criminal action against" , "Bring before a criminal court" .)