Heartless German soldier pinches used, sleeveless jumper (6)
I believe the answer is:
jersey
'jumper' is the definition.
(I've seen this before)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for jersey that I've seen before include "Garment - cow - island" , "Milked" , "Something one may put on" , "Pullover; an island" , "One of the Channel Islands" .)