An assembly for braking the displacement of a tailpipe cover is disclosed. The assembly has a clamping element with an elastic material, a tailpipe, and a tailpipe cover. The clamping element is arranged at least indirectly on the tailpipe and on the tailpipe cover. A section of the clamping element extends over the tailpipe in the axial direction parallel to the longitudinal axis of the tailpipe cover. The distance between the longitudinal axis and the clamping element is designed to be at least partly shorter than the distance between the longitudinal axis and the tailpipe in said clamping element section. Alternatively or in addition thereto, at least one section of the clamping element is arranged at least indirectly against the tailpipe in an immovable manner in the direction of the longitudinal axis.