old hand vs expert

old hand and expert both are nouns.

Word	Noun	Adjective	Verb	Adverb
old hand	Yes	No	No	No
expert	Yes	Yes	No	No

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

old hand: an experienced person who has been through many battles; someone who has given long service
expert: a person with special knowledge or ability who performs skillfully

old hand (noun)	expert (noun)
an experienced person who has been through many battles; someone who has given long service	a person with special knowledge or ability who performs skillfully

old hand (adjective)	expert (adjective)
	having or showing knowledge and skill and aptitude
	of or relating to or requiring special knowledge to be understood