I'm looking for a word that conveys that an organization (but more generally could include a person) has jurisdiction over something. What would I call, in general, the organization which has jurisdiction?
An agency or body created by a government to perform a specific function, such as environment management, power generation, or tax collection.
(often authorities) A person or organization having political or administrative power and control:
health authorities issued a worldwide alert
Apart from the politicians and the health authorities, economists are also worried.
These, then, are the various powers under which governmental authorities may act.
They are also calling for powers to allow authorities to intervene to protect young people who are at risk from drugs.
officials, officialdom, the people in charge, the government, the administration, the establishment, the bureaucracy, the system; the police
informal the powers that be, the (men in) suits, Big Brother
You could say they're the administrator:
a person responsible for running a business, organization, etc.
synonyms: manager, director, executive, controller, head, chief, leader, governor, superintendent, supervisor; boss
"he became the team's top administrator in 1973"
Similarly, you could call them the administration, depending on exactly what you're talking about.