escalate

To escalate a problem is to pass it up to somebody more senior. The person in front of you cannot help, so it goes higher.

That customer-service sense is now the commonest in working life: escalate the ticket, escalate it to a manager. The older meaning is about growing worse, and a dispute that escalates gets steadily bigger — an escalating conflict, escalating costs. Both go back to escalator, and the picture is the same in each, of something carried steadily upward. The noun is escalation.