Alien president began to proclaim (7)
I believe the answer is:
trumpet
'to proclaim' is the definition.
(I know that trumpet is a kind of exclaim)
'alien president began' is the wordplay.
I cannot really understand how this works, but
'alien' could be 'et' (extra terrestrial) and 'et' is located in the answer.
'president' could be 'trump' (Donald Trump) and 'trump' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for trumpet that I've seen before include "beastly noise" , "Daffodil corona" , "Brass wind instrument" , "Orchestral or military instrument" , "Metal wind instrument" .)