peeress vs adult female

peeress and adult female both are nouns.

Word	Noun	Adjective	Verb	Adverb
peeress	Yes	No	No	No
adult female	Yes	No	No	No

As nouns, adult female is a hypernym of peeress; that is, adult female is a word with a broader meaning than peeress:

Other hypernyms of peeress include female aristocrat, woman.

peeress (noun)	adult female (noun)
a woman of the peerage in Britain	an adult female person (as opposed to a man)