Left-leaning socialist near English city (5)
I believe the answer is:
derby
'english city' is the definition.
(I've seen this before)
'left-leaning socialist near' is the wordplay.
'left-leaning' says the letters should be written backwards (letters written right to left).
'socialist' becomes 'red' (red can informally mean a socialist).
'near' becomes 'by' (near means close by).
'red' reversed gives 'der'.
'der'+'by'='DERBY'
(Other definitions for derby that I've seen before include "Epsom horse race" , "... and after 8 [STATE = KENTUCKY] , meeting" , "Local game" , "Midlands city" , "Flat race; hat" .)