Exaggerated praise a drag (4)
I believe the answer is:
puff
I believe this clue is a double definition.
'exaggerated praise' is the first definition.
'a drag' is the second definition.
('puff' can be a synonym of 'drag')
(Other definitions for puff that I've seen before include "Light < case" , "Exaggerated praise (for promotional purposes?)" , "Pull" , "promotion" , "Advertisement; smoke a cigarette" .)