The present invention relates to devices and methods for improving the function of a defective heart valve, and particularly for reducing regurgitation through an atrioventricular heart valve—i.e., the mitral valve and the tricuspid valve. For a tricuspid repair, the device includes an anchor deployed in the tissue of the right ventricle, in an orifice opening to the right atrium, or anchored to the tricuspid valve. A flexible anchor rail connects to the anchor and a coaptation element on a catheter rides over the anchor rail. The catheter attaches to the proximal end of the coaptation element, and a locking mechanism fixes the position of the coaptation element relative to the anchor rail. Finally, there is a proximal anchoring feature to fix the proximal end of the coaptation catheter subcutaneously adjacent the subclavian vein. The coaptation element includes an inert covering and helps reduce regurgitation through contact with the valve leaflets.