urgency has 2 distinct synonyms spread across 1 of its 4 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the state of being urgent; an earnest and insistent necessity
pressing importance requiring speedy action
“the urgency of his need”
Synonyms, antonyms and the broader and narrower relations for urgency come from Princeton University’s WordNet. Full sources and licences.
an urgent situation calling for prompt action
“I'll be there, barring any urgencies”
insistent solicitation and entreaty
“his importunity left me no alternative but to agree”