In this letter, the posterior Cram\’{e}r-Rao lower bounds (PCRLB) for three-dimensional (3D) star-convex shaped extended target tracking (3D-ETT) is proposed to quantify the accuracy of the extended target state estimation within the Gaussian process (GP) framework.In view of the complex interdependence between the 3D target pose and the extent description, the PCRLB recursion of translation, rotation and extent states is derived.The resulting PCRLB are compared on simulation with the performance of the ETT algorithms using the GP for extent estimation.