New Dealer vs admirer

New Dealer and admirer both are nouns.

Word	Noun	Adjective	Verb	Adverb
New Dealer	Yes	No	No	No
admirer	Yes	No	No	No

As nouns, admirer is a hypernym of New Dealer; that is, admirer is a word with a broader meaning than New Dealer:

New Dealer: a supporter of the economic policies in the United States known as the New Deal
admirer: a person who backs a politician or a team etc.

Other hypernyms of New Dealer include booster, champion, friend, protagonist, supporter.

New Dealer (noun)	admirer (noun)
a supporter of the economic policies in the United States known as the New Deal	someone who admires a young woman
	a person who backs a politician or a team etc.
	a person who admires; someone who esteems or respects or approves