A separator includes a rotatable drum having a vertical rotational axis, a disk stack arranged in the drum, an inner gripper and an outer gripper that do not rotate with the drum are configured to discharge mutually-separated liquid phases. A discharge line is assigned to each gripper and is arranged in an associated gripper chamber of the drum. The inner gripper includes an inner gripper shaft and the outer gripper includes an outer gripper shaft both of which shafts protrude axially from the drum. Each associated gripper chamber, with its associated gripper, revolves on different radii with respect to the rotational axis such that a chamber is formed radially between an outer circumference of the inner gripper shaft and an inner circumference of the outer gripper shaft. A fluid is insertable into the chamber through a channel, which fluid is pressable from the chamber into the gripper chambers.