A flexible clamping insert for adapting the clamping contour of a clamping device to correspond to an outer contour of a bicycle frame. The clamping insert includes a mounting section, a pivoting section and a biasing section connecting the mounting section and the pivoting section. The clamping insert is formed as one piece from a flexible material. The mounting section includes at least one attachment feature for securing the mounting section to a fixed clamping arm of the clamping device. The mounting and pivoting sections have a concave contour and the biasing section has a convex, resulting in the clamping insert, in the uninstalled state, having a C-shaped contour. When installed on the clamping device, the biasing section biases the pivoting section toward an open position, resulting in the pivoting arm to open and allow the clamping insert and device to be mounted on to the bicycle frame. The one-piece clamping insert is cost-effective and is simple to snap onto the clamping device without the use of tools.