Shame city centre's controlled by party extremists (4)
I believe the answer is:
pity
'shame' is the definition.
(synonyms)
'city centre's controlled by party extremists' is the wordplay.
'city centre' becomes 'it' (centre of the word 'city').
'controlled by' means one lot of letters goes inside another (some letters restrict or block in others).
'extremists' means to remove the middle letters.
'party' with its middle removed is 'py'.
'it' put within 'py' is 'PITY'.
(Other definitions for pity that I've seen before include "Mercy" , "Sympathy and sorrow" , "Sorrow, compassion" , "Sympathise with" , "Feel sorrow for" .)