Old and sick, a politician needs light (3,4)
I believe the answer is:
oil lamp
'light' is the definition.
(oil lamp is a kind of light)
'old and sick a politician' is the wordplay.
'old' becomes 'o' (abbreviation).
'and' says to put letters next to each other.
'sick' becomes 'ill' (similar in meaning).
'politician' becomes 'MP' (Member of Parliament).
'o'+'ill'+'a'+'mp'='OIL-LAMP'
'needs' is the link.
(Other definitions for oil lamp that I've seen before include "Early means of illumination" , "Light that burns kerosene" .)