The Parisienne cut fur for part of a coat (5)
I believe the answer is:
lapel
'part of a coat' is the definition.
(I've seen this before)
'the parisienne cut fur' is the wordplay.
'the parisienne' becomes 'la'.
'cut' means to remove the last letter.
'fur' becomes 'pelt' ('pelt' can be a synonym of 'fur').
'pelt' with its last letter taken off is 'pel'.
'la'+'pel'='LAPEL'
'for' is the link.
(Other definitions for lapel that I've seen before include "Continuation of a coat collar" , "Folded-back part of coat" , "Jacket fold" , "Part of a folded back collar" , "Revere on a coat" .)