Person in court's simple dispute (9)
I believe the answer is:
plaintiff
'person in court's' is the definition.
'simple dispute' is the wordplay.
'simple' becomes 'plain' (synonyms).
'dispute' becomes 'tiff' (tiff is a kind of dispute).
'plain'+'tiff'='PLAINTIFF'
(Other definitions for plaintiff that I've seen before include "The one taking the court action" , "Person bringing a court case" , "Temporary disappearances of a heavenly body" , "Person bringing a civil action in a court of law" , "one in suit" .)