River bridge piers may collapse due to the local scour around their foundations. It is known that local scour is an effect of the three-dimensional flow field that develops near the pier and that the geometric complexity of a non-cylindrical pier may, correspondingly, increase the complexity of the process. It is also known that various devices may be used as scour countermeasures. This manuscript explores the use of a bed sill as a countermeasure for local scour at a complex bridge pier compound of an array of piles, a pile cap, and two inclined columns with the rectangular sections above the cap. This pier geometry, never studied before in combination with a scour countermeasure, was stimulated by an existing bridge. Different sill placements were tested (at the upstream or downstream edges of the pier, or in an intermediate position) for various values of the pile diameter and number, cap thickness and cap elevation. The results of a wide experimental campaign consistently showed that the most effective placement of the transverse sill was at the upstream edge of the pier, for which scour reductions of up to 30–40% could be obtained for the long-term scour depth. The countermeasure performance decreased to about 10% when the sill was placed at the downstream edge of the pier. Furthermore, the installation of a transverse sill upstream of the pier also changed the shape of the scour hole because the pier was then located in an area prone to sill scour; however, for the present experiments, the combination of the effects was beneficial in terms of the resulting scour depth. Although the investigation of a single hydro-dynamic condition prevents the experimental findings from being generalized, the promising results stimulate further consideration of a transverse sill as a countermeasure for local scour at a complex pier.