ESRF is a state of the art third generation synchrotron light source optimized to produce very bright and collimated hard X-ray beams using insertion devices. Instabilities of the electron beam, resulting in source point transverse displacements, spoil these outstanding beam qualities. At the beginning of operation a fast active feedback system was installed to damp the transverse motion of the electron beam in the vertical plane. Recently it became evident that also the relatively smaller horizontal instabilities may have specific detrimental effects on the operation of particularly sensitive beamlines. The dispersive XAS beamline (ID24) was the first to benefit from the activation of a local horizontal feedback. Optimized to perform time-resolved studies and high-pressure experiments, its operation was strongly perturbed. This paper briefly describes the work carried out to identify and solve these problems, presenting the outcome of the implementation of a fast orbit feedback on this beamline.