Exaggerate — blow up (7)
I believe the answer is:
inflate
I believe this is a double definition.
'exaggerate' is the first definition.
(I've seen this in another clue)
'blow up' is the second definition.
(synonyms)
(Other definitions for inflate that I've seen before include "aggrandize them" , "Puff up" , "Exaggerate or fill with air" , "Expand unduly" , "Enlarge" .)