old vs yesteryear

old and yesteryear both are nouns.

Word	Noun	Adjective	Verb	Adverb
old	Yes	Yes	No	No
yesteryear	Yes	No	No	No

As nouns, yesteryear is a hypernym of old; that is, yesteryear is a word with a broader meaning than old:

Other hypernyms of old include past, past times.

old (noun)	yesteryear (noun)
past times	the time that has elapsed

old (adjective)	yesteryear (adjective)
of long duration; not new
(used especially of persons) having lived for a relatively long time or attained a specific age
skilled through long experience
(used for emphasis) very familiar
excellent
just preceding something else in time or order
belonging to some prior time