supremacy vs ascendancy

supremacy and ascendancy both are nouns.

Word	Noun	Adjective	Verb	Adverb
supremacy	Yes	No	No	No
ascendancy	Yes	No	No	No

As nouns, ascendancy is a hypernym of supremacy; that is, ascendancy is a word with a broader meaning than supremacy:

supremacy: power to dominate or defeat
ascendancy: the state that exists when one person or group has power over another

Other hypernyms of supremacy include ascendance, ascendence, ascendency, control, dominance.

supremacy (noun)	ascendancy (noun)
power to dominate or defeat	the state that exists when one person or group has power over another