Last broadcast by elected Soviet leader (6)
I believe the answer is:
stalin
'soviet leader' is the definition.
(I've seen this before)
'last broadcast by elected' is the wordplay.
'broadcast' indicates an anagram.
'by' is a charade indicator (letters next to each other).
'elected' becomes 'in'.
'last' anagrammed gives 'stal'.
'stal'+'in'='STALIN'
(Other definitions for stalin that I've seen before include "Tyrannical dictator among Latins" , "Former Georgian theology student, d. 1953" , "Russian WW two leader" , "Dreaded dictator among Latins" , "Bolshevik" .)