Quiet socialist has scrap (5)
I believe the answer is:
shred
'scrap' is the definition.
(both can mean a small amount of material)
'quiet socialist' is the wordplay.
'quiet' becomes 'sh' ('sh' is used to tell someone to be quiet).
'socialist' becomes 'red' (red can informally mean a socialist).
'sh'+'red'='SHRED'
'has' is the link.
(Other definitions for shred that I've seen before include "Cut into tiny pieces" , "Tear into tiny pieces" , "Tatter; small amount" , "Cut into small pieces" , "Strip of material; a very small amount" .)