End of Third World famine (6)
I believe the answer is:
dearth
'famine' is the definition.
(a famine is a dearth of food)
'end of third world' is the wordplay.
'end of' says to take the final letters.
'world' becomes 'earth' (synonyms).
The last letter of 'third' is 'd'.
'd'+'earth'='DEARTH'
(Other definitions for dearth that I've seen before include "Lack of resources" , "Acute insufficiency" , "Hatred (anag) -- shortage" , "Shortage, lack" , "deficiency" .)