urgency

(noun) the state of being urgent; an earnest and insistent necessity.

(noun) pressing importance requiring speedy action. Example: "The urgency of his need."

(noun) an urgent situation calling for prompt action. Examples: "I'll be there, barring any urgencies." "They departed hurriedly because of some great urgency in their affairs."

(noun) insistent solicitation and entreaty. Synonyms: importunity, urging. Example: "His importunity left me no alternative but to agree."