Fine composer docked next to big city (6)
I believe the answer is:
satiny
'fine' is the definition.
(thesaurus)
'composer docked next to big city' is the wordplay.
'composer' becomes 'satie' (French composer Erik Satie).
'docked' means to remove the last letter (to dock can mean to remove the tail of an animal).
'next to' says to put letters next to each other.
'big city' becomes 'NY' (New York).
'satie' with its final letter removed is 'sati'.
'sati'+'ny'='SATINY'
(Other definitions for satiny that I've seen before include "smooth result?" , "having a smooth, gleaming surface" , "shiny and lustrous" , "Sanity (anag.)" , "Smooth and glossy" .)