Teleoperation is still the de-facto mode of operation for robotic manipulators in hazardous and unknown environments. The objective is to move the manipulator under the influence of a plenitude of constraints, mainly following the human operator’s commands, but also the avoidance of adverse effects such as joint limits or the exertion of external forces. A classic approach to incorporate such non-instantaneous behavior into the instantaneous motion of the kinematic chain is the Closed-Loop Inverse Kinematics (CLIK) control scheme. In this paper, we present PV-CLIK, a novel CLIK realization that for the first time practically applies the Popov- Vereshchagin (PV) hybrid dynamics solver to map the instan- taneous constraints to motion commands. By relying on the PV solver, PV-CLIK offers several benefits over traditional CLIK implementations such as linear runtime complexity, handling constraints on the dynamics level or fostering composable software architectures. In the experimental evaluation, we show that our implementation of PV-CLIK outperforms existing kinematics solvers in Cartesian trajectory-following tasks at high velocities.