Rest stupidly in activity, getting left behind (8)
I believe the answer is:
deserted
'left behind' is the definition.
(deserting is a kind of leaving behind)
'rest stupidly in activity' is the wordplay.
'stupidly' indicates an anagram.
'in' indicates putting letters inside.
'activity' becomes 'deed' (I've seen this in other clues**).
'rest' anagrammed gives 'sert'.
'sert' put into 'deed' is 'DESERTED'.
'getting' acts as a link.
(Other definitions for deserted that I've seen before include "Empty of people" , "uncultivated" , "Left the armed forces without permission" , "Left the armed forces illegally" , "Illegally left army" .)