If I correctly understand the question, this is generally described as an appellate court upholding or affirming the lower court's rulings.
Whatever appellate court is immediately above the trial court in that particular court system.
Appellate court.
Appellate jurisdicton
Usually it is, except that in New York State, the trial court is called the Supreme Court and the highest court is called the Court of Appeals. There is an intermediate appellate court called the Appellate Division.
A Circuit.
An appellate court reverses the decision
An appellate court reverses the decision
An appellate court reverses the decision
The authority of a court to hear a case is its jurisdiction.
Appellate court
It's called appellate jurisdiction.
Typically, the Appellate Court will either uphold a conviction or reverse and remand (meaning the case goes back to the lower court for a new hearing on the merits).