Shroud one round Conservative lying in state (7)
I believe the answer is:
conceal
'shroud' is the definition.
(I've seen this in another clue)
'one round conservative lying in state' is the wordplay.
'round' indicates putting letters inside.
'conservative' becomes 'C' (UK political abbreviation).
'lying in' indicates putting letters inside.
'state' becomes 'cal' (short for California).
'one' going around 'c' is 'once'.
'once' put within 'cal' is 'CONCEAL'.
(Other definitions for conceal that I've seen before include "hush up!" , "'Hide, keep secret (7)'" , "Place out of sight" , "Keep out of sight" , "Screen" .)