exigent
Meaning: urgent, critical
Usage: The patient has an exigent need for medication, or else he will lose his sight.
imperative
Meaning: absolutely necessary; urgent
Usage: It was imperative that the team repair the bridge before nightfall.
pressing
Meaning: requiring immediate attention
Usage: The mayor postponed routine meetings to address the city’s pressing water problem.
dire
Meaning: extremely serious or urgent
Usage: The hikers faced a dire situation when their last water bottle cracked.
critical
Meaning: extremely important or serious
Usage: The final rehearsal was critical to the success of the performance.