An arrangement for gripping end regions of an elongated flexible element extended between support surfaces, comprises a casing having an interior passage, and an inner conically-shaped wall, and a movable sleeve mounted for axial movement relative to the casing. The sleeve has an axial channel through which the element is inserted, an outer conically-shaped body, and at least one radial hole in the outer body. At least one gripping member is mounted in the radial hole of the sleeve. The radial dimension of the gripping member is larger than the radial length of the radial hole. The gripping member is movable from a non-gripping position in which the gripping member is located outside the channel, to a gripping portion in which the gripping member is pushed by the inner wall to extend into the channel for gripping the inserted end region of the element.