Outfit that tried to get people talking of postage fiddle (7)
I believe the answer is:
'outfit that tried to get people talking' is the definition.
(Nazi secret police who made prisoners talk)
'postage fiddle' is the wordplay.
'fiddle' is an anagram indicator.
'postage' anagrammed gives 'GESTAPO'.
'of' is the link.
(Other definitions for gestapo that I've seen before include "State police in Nazi Germany" , "Postage to Nazi secret police" , "war force" , "Postage for Hitler's police" , "Police detested" .)