It provides illumination for the French politician (4)
I believe the answer is:
lamp
'it provides illumination' is the definition.
The definition suggests a singular noun which matches the answer.
'the french politician' is the wordplay.
'the french' becomes 'la' (one of the French words for 'the').
'politician' becomes 'MP' (Member of Parliament).
'la'+'mp'='LAMP'
'for' acts as a link.
Can you help me to learn more?
(Other definitions for lamp that I've seen before include "Source of light, usually portable" , "bulb" , "Source of artificial light" , "Device for giving light on palm" , "Aladdin's - -" .)