necessity vs exigency

necessity and exigency both are nouns.

Word	Noun	Adjective	Verb	Adverb
necessity	Yes	No	No	No
exigency	Yes	No	No	No

As nouns, exigency is a hyponym of necessity; that is, exigency is a word with a more specific, narrower meaning than necessity:

necessity: the condition of being essential or indispensable
exigency: that which is required in a particular situation —usually used in plural.

Other hyponyms of necessity include requisiteness, urgency.

necessity (noun)	exigency (noun)
anything indispensable	a sudden unforeseen crisis (usually involving danger) that requires immediate action
the condition of being essential or indispensable	a pressing or urgent situation
	that which is required in a particular situation —usually used in plural.