Ham finished with a case of claret (7)
I believe the answer is:
overact
'ham' is the definition.
('overact' can be a synonym of 'ham')
'finished with a case of claret' is the wordplay.
'finished' becomes 'over' ('over' can be similar in meaning to 'finished').
'with' says to put letters next to each other.
'case of' says to hollow out the word (remove centre letters) (outsides of).
'claret' with its middle removed is 'ct'.
'over'+'a'+'ct'='OVERACT'
(Other definitions for overact that I've seen before include "Perform with exaggeration" , "Exaggerate" , "Cartoon twenty four across" , "In part, fail to convince" , "Play part exaggeratedly" .)