Propose an item broadcast after drama (8)
I believe the answer is:
nominate
'propose' is the definition.
('nominate' can be a synonym of 'propose')
'an item broadcast after drama' is the wordplay.
'broadcast' is an anagram indicator.
'after' means one lot of letters go next to another.
'drama' becomes 'no' (Noh or No is a Japanese masked drama).
'an'+'item'='anitem'
'anitem' anagrammed gives 'minate'.
'minate' after 'no' is 'NOMINATE'.
(Other definitions for nominate that I've seen before include "Propose as a candidate" , "Pick as a candidate" , "Choose" , "Designate" , "Propose - name" .)