Exaggerate, having finished act (6)
I believe the answer is:
overdo
'exaggerate' is the definition.
(synonyms)
'finished act' is the wordplay.
'finished' becomes 'over' (similar in meaning).
'act' becomes 'do' (to do is to act or execute a task).
'over'+'do'='OVERDO'
'having' acts as a link.
(Other definitions for overdo that I've seen before include "Maybe burn" , "Exaggerate; use too much of" , "Exhaust" , "Cook too long or act excessively" , "Use too much of (something)" .)