Foolish speech: beaten President absolutely losing head (8)
I believe the answer is:
trumpery
'foolish speech' is the definition.
'beaten president absolutely losing head' is the wordplay.
'beaten president' becomes 'trump' (Donald Trump).
'absolutely' becomes 'very' (I've seen this before).
'losing head' means to remove the first letter.
'very' with its first letter taken off is 'ery'.
'trump'+'ery'='TRUMPERY'
(Other definitions for trumpery that I've seen before include "rubbish" , "presidential tweets, say" , "Foolish, worthless talk or actions" , "Worthless trinkets" , "Worthless (thing)" .)