An insert element fastens to an annular segment body of a turbine of a gas turbine. The annular segment body has a recess on a hot-gas side. The insert element is designed to cover the recess and has a concave front side and a rear side having at least one shaped portion for positioning on the annular segment body. An annular segment has the insert element, a gas turbine has the insert element, and a mounting method mounts the insert element.