local government vs authorities

local government and authorities both are nouns.

Word	Noun	Adjective	Verb	Adverb
local government	Yes	No	No	No
authorities	Yes	No	No	No

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

local government: the government of a local area
authorities: the organization that is the governing authority of a political unit

Other hypernyms of local government include government, regime.

local government (noun)	authorities (noun)
the government of a local area	the organization that is the governing authority of a political unit