Which NIMS Management Characteristic refers to personnel requested through appropriate authorities and established resource management systems?

The answer is "Dispatch / Deployment".

Assets not requested must not self-dispatch to abstain from overloading the incident command. NIMS which stands for National Incident Management System is a methodical, proactive way to deal with manage all levels of government, nongovernmental associations (NGOs), and the private segment to cooperate to avoid, ensure against, moderate, react to, and recoup from the impacts of incidents.