Give up performing encore with French article (8)
I believe the answer is:
renounce
'give up' is the definition.
('renounce' can be a synonym of 'give up')
'performing encore with french article' is the wordplay.
'performing' indicates anagramming the letters.
'with' indicates putting letters inside.
'french article' becomes 'un' (French for 'a' - the indefinite article).
'encore' with letters rearranged gives 'renoce'.
'renoce' placed around 'un' is 'RENOUNCE'.
(Other definitions for renounce that I've seen before include "Disclaim or reject publicly" , "Give up, abdicate" , "Formally give up" , "Give up, turn away from" , "Reject, perhaps the devil" .)