Edges to lightly cover with a stretchy fabric (5)
I believe the answer is:
lycra
'stretchy fabric' is the definition.
(I've seen this before)
'edges to lightly cover with a' is the wordplay.
'edges to' means to remove the middle letters (only letters at the edges of the word).
'cover with' becomes 'cr' (I can't justify this - if you can you should believe this answer much more).
'lightly' with its centre removed is 'ly'.
'ly'+'cr'+'a'='LYCRA'
(Other definitions for lycra that I've seen before include "Spandex" , "clinging fabric" , "Material for exercise wear" , "synthetic fibre" , "Elasticated synthetic material" .)