Anguish of the Gascon duo (7)
I believe the answer is:
despair
'anguish' is the definition.
(thesaurus)
'of the gascon duo' is the wordplay.
'of the gascon' becomes 'des' (can mean 'of the' in French, eg in Gascony).
'duo' becomes 'pair' ('pair' can be a synonym of 'duo').
'des'+'pair'='DESPAIR'
(Other definitions for despair that I've seen before include "Praised (anag) - lose hope" , "displaying lack of optimism" , "Resignation" , "Total loss of hope" , "First appearance" .)