In former president's way, excluding old part of US (7)
I believe the answer is:
alabama
'part of us' is the definition.
('Alabama' is part of 'us')
I don't understand how the rest of the clue works.
(Other definitions for alabama that I've seen before include "US state in which Birmingham is situated" , "American state, capital Montgomery (7)" , "Birmingham area" , "Somewhere in US" , "where cotton can be produced" .)