Heart of Polish politician yielding (4)
I believe the answer is:
limp
'yielding' is the definition.
(both can mean pliable or slack)
'heart of polish politician' is the wordplay.
'heart of' means to look at the middle letters.
'politician' becomes 'MP' (Member of Parliament).
The central letters of 'polish' are 'li'.
'li'+'mp'='LIMP'
(Other definitions for limp that I've seen before include "Slack, wilted" , "Saggy and drooping" , "Walk badly; not stiff" , "Walk with an uneven stop" , "Hanging loosely - hobble" .)