Around US state, Marxist stayed (8)
I believe the answer is:
remained
'stayed' is the definition.
('remain' can be a synonym of 'stay')
'around us state marxist' is the wordplay.
'around' indicates putting letters inside.
'us state' becomes 'maine' (I've seen this before).
'marxist' becomes 'red' ('red' can be a synonym of 'marxist').
'maine' going inside 'red' is 'REMAINED'.
(Other definitions for remained that I've seen before include "Was left" , "Stayed put as I meander" , "didn't move" , "Stayed behind" .)