Insist staff sunbathe -- one's covered up twice (8)
I believe the answer is:
maintain
'insist' is the definition.
(maintaining is a kind of insisting)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for maintain that I've seen before include "Keep in existence or in repair" , "Keep going" , "Keep in safety and protect from harm and decay" , "Look after the upkeep" , "Conserve" .)