Red Queen cutting finger (4)
I believe the answer is:
trot
'red' is the definition.
(Trotskyite, type of socialist or 'red')
'queen cutting finger' is the wordplay.
'queen' becomes 'r' (abbreviation for regina, e.g. in ER ).
'cutting' means one lot of letters goes inside another (some letters cut their way into a word).
'finger' becomes 'tot' (both are a small amount of alcohol).
'r' going within 'tot' is 'TROT'.
(Other definitions for trot that I've seen before include "Move at brisk pace" , "Brisk movement" , "Fairly fast pace of a horse" , "(Horse's) moderate pace" , "Gait between a walk and a canter" .)