1. increase rapidly, bring an issue to someone of a higher rank
escalate costs/a complaint/issue
The verb to escalate can mean to increase and in number or volume rapidly. Someone's temperature might escalate if they are sick, for example, or the numbers of people in employment could escalate. If something escalates it can also become more serious or pressing. So a problem can escalate or tension can escalate, for example. To escalate a problem/matter/complaint can mean to involve someone higher up or more senior in order to address a problem.