Make hanging smoother? That was bad for international relations (4,7)
I believe the answer is:
iron curtain
'that was bad for international relations' is the definition.
(the iron curtain divided the West and the USSR)
'make hanging smoother?' is the wordplay.
I cannot quite see how this works, but
'hanging' could be 'curtain' and 'curtain' is found in the answer.
'smoother?' could be 'iron' (I've seen this in another clue) and 'iron' is found within the answer.
No letters remain.
This explanation may well be incorrect...
(Other definitions for iron curtain that I've seen before include "Old barrier between East & West Europe" , "What divided European sides" , "Notional barrier between East and West" , "Impenetrable barrier" , "Former barrier across Europe" .)