Flush at socialist study (6)
I believe the answer is:
redden
'flush' is the definition.
(I know that flush can be written as redden)
'at socialist study' is the wordplay.
'at' is a charade indicator (letters next to each other).
'socialist' becomes 'red' (socialism is often associated with the colour red).
'study' becomes 'den' (term for a study or office).
'red' next to 'den' is 'REDDEN'.
(Other definitions for redden that I've seen before include "Reveal embarrassment in colourful way" , "Blush, colour accordingly" , "Give visible sign of embarrassment" , "Flush, become embarrassed" , "Blush or become flushed" .)