Socialist at United Church cut down (6)
I believe the answer is:
reduce
'cut down' is the definition.
(I know that cut down can be written as reduce)
'socialist at united church' is the wordplay.
'socialist' becomes 'red' (socialism is often associated with the colour red).
'at' means one lot of letters go next to another.
'united' becomes 'U' (abbreviation as in Man U for Manchester United).
'church' becomes 'CE' (abbreviation for Church of England).
'red'+'u'+'ce'='REDUCE'
(Other definitions for reduce that I've seen before include "Of a sauce, thicken" , "diet" , "Lower" , "Make smaller or lose weight" , "Shrink" .)