Fabric in garment covering end of zipper (5)
I believe the answer is:
crape
'fabric' is the definition.
(crape is a kind of fabric)
'garment covering end of zipper' is the wordplay.
'garment' becomes 'cape' (cape is a kind of garment**).
'covering' is an insertion indicator.
'end of' indicates one should take the final letters.
The last letter of 'zipper' is 'r'.
'cape' placed around 'r' is 'CRAPE'.
'in' acts as a link.
(Other definitions for crape that I've seen before include "Fabric" , "band for a funeral" .)