The French knight admitted to relative indulgence (8)
I believe the answer is:
lenience
'indulgence' is the definition.
('lenience' can be a synonym of 'indulgence')
'the french knight admitted to relative' is the wordplay.
'the french' becomes 'le'.
'knight' becomes 'n' (chess).
'admitted to' means one lot of letters goes inside another.
'relative' becomes 'niece' (niece is a kind of relative**).
'n' put inside 'niece' is 'nience'.
'le'+'nience'='LENIENCE'
(Other definitions for lenience that I've seen before include "Tolerance" , "indulgence" , "Quality of mercy in awarding punishment" .)