local vs anesthetic agent

local and anesthetic agent both are nouns.

Word	Noun	Adjective	Verb	Adverb
local	Yes	Yes	No	No
anesthetic agent	Yes	No	No	No

As nouns, anesthetic agent is a hypernym of local; that is, anesthetic agent is a word with a broader meaning than local:

Other hypernyms of local include anaesthetic, anaesthetic agent, anesthetic.

local (noun)	anesthetic agent (noun)
public transport consisting of a bus or train that stops at all stations or stops	a drug that causes temporary loss of bodily sensations
anesthetic that numbs a particular area of the body

local (adjective)	anesthetic agent (adjective)
relating to or applicable to or concerned with the administration of a city or town or district rather than a larger area
affecting only a restricted part or area of the body
of or belonging to or characteristic of a particular locality or neighborhood