Sheer class (4)
I believe the answer is:
rank
I believe this clue is a double definition.
'sheer' is the first definition.
('rank' can be a synonym of 'sheer')
'class' is the second definition.
(I have seen 'Social class ' mean 'rank' so perhaps 'class' could also mean 'rank')
(Other definitions for rank that I've seen before include "Violent old-fashioned" , "The military row is coarsely overgrown" , "(Taxi) stand" , "Status; foul" , "Level; smelling bad" .)