Show shame at socialist study (6)
I believe the answer is:
redden
'show shame' is the definition.
Although both the answer and definition are verbs in their base form, I cannot see how one could define the other.
'at socialist study' is the wordplay.
'at' says to put letters next to each other.
'socialist' becomes 'red' (red is a kind of socialist).
'study' becomes 'den' (I've seen this before**).
'red' put next to 'den' is 'REDDEN'.
Can you help me to learn more?
(Other definitions for redden that I've seen before include "Give visible sign of embarrassment" , "Blush, colour accordingly" , "Flush, become embarrassed" , "Group of states under one head" , "Blush like the dawn sky" .)