Gifted by The French National Gallery without director (8)
I believe the answer is:
talented
'gifted' is the definition.
(synonyms)
'the french national gallery without director' is the wordplay.
'the french' becomes 'le' ('the' in French).
'national' becomes 'n' (abbreviation listed in Chambers).
'gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'without' indicates putting letters inside.
'director' becomes 'd'.
'le'+'n'='len'
'len' inserted within 'tate' is 'talente'.
'talente'+'d'='TALENTED'
'by' is the link.
(Other definitions for talented that I've seen before include "Brilliant" , "Possessing aptitude" , "Able" , "Having special or great ability" , "Showing a natural aptitude" .)