What is the name of the order from the court that directs an official to perform a specific act?

The correct answer, mandate, refers specifically to a court order that directs an official or entity to perform a particular action or fulfill a duty as required by law or rule. In legal contexts, mandates are authoritative commands that compel action, ensuring that certain procedures are followed or that specific tasks are executed.

A summons is a legal document that notifies a person of their involvement in a legal proceeding and requires them to appear in court, which does not align with the definition of directing an official to perform an act. A resolution typically refers to a formal decision made by a legislative body or organization, rather than a court order directed at a specific official. An edict is a formal proclamation or command issued by an authority, which can be broader and does not specifically denote a court order like a mandate does.

Therefore, the term "mandate" captures the essence of the court's directive nature, making it the correct answer in this context.