high-up vs important person

high-up and important person both are nouns.

Word	Noun	Adjective	Verb	Adverb
high-up	Yes	No	No	No
important person	Yes	No	No	No

As nouns, important person is a hypernym of high-up; that is, important person is a word with a broader meaning than high-up:

high-up: an important or influential (and often overbearing) person
important person: a person whose actions and opinions strongly influence the course of events

Other hypernyms of high-up include influential person, personage.

high-up (noun)	important person (noun)
an important or influential (and often overbearing) person	a person whose actions and opinions strongly influence the course of events