Chef Raymond overcoming skin complaint to provide dessert (10)
I believe the answer is:
blancmange
'dessert' is the definition.
(blancmange is a kind of dessert)
'chef raymond overcoming skin complaint' is the wordplay.
'chef raymond' becomes 'Blanc' (Raymond Blanc is a French chef).
'overcoming' is a charade indicator (letters next to each other) (some letters are written over others).
'skin complaint' becomes 'mange' (mange is an animal skin disease).
'blanc'+'mange'='BLANCMANGE'
'to provide' is the link.
(Other definitions for blancmange that I've seen before include "Jelly-like pudding made with milk" , "Dessert of flavoured milk stiffened with cornflower" , "Almond-flavoured jelly-like milk pudding" , "Wobbly dessert" , "group?" .)