Socialist cue about to diminish (6)
I believe the answer is:
reduce
'diminish' is the definition.
(reducing is a kind of diminishing)
'socialist cue about' is the wordplay.
'socialist' becomes 'red' (red is a kind of socialist).
'about' indicates an anagram.
'cue' is an anagram of 'uce'.
'red'+'uce'='REDUCE'
'to' is the link.
(Other definitions for reduce that I've seen before include "Shrink" , "Bring down" , "Decrease" , "Make smaller or slim down" , "Make smaller or lose weight" .)