Woven fabric for tailored suits with fine finish (6)
I believe the answer is:
tissue
'woven fabric' is the definition.
'tailored suits with fine finish' is the wordplay.
'tailored' indicates anagramming the letters (the letters are customised ).
'with' says to put letters next to each other.
'finish' indicates one should take the final letters.
The final letter of 'fine' is 'e'.
'suits' is an anagram of 'tissu'.
'tissu'+'e'='TISSUE'
'for' is the link.
(Other definitions for tissue that I've seen before include "Sneeze catcher?" , "Type of paper" , "used to make up lies?" , "Gauzy fabric" , "Delicate fabric" .)