Pursuing prey through clutter is a complex and risky activity requiring integration of guidance subsystems for obstacle avoidance and target pursuit. The unobstructed pursuit trajectories of Harris' hawks Parabuteo unicinctus are well modelled by a mixed guidance law feeding back target deviation angle and line-of-sight rate. Here we ask how their closed-loop pursuit behavior is modified in response to obstacles, using high-speed motion capture to reconstruct flight trajectories recorded during obstructed pursuit of maneuvering targets. We find that their trajectories are well modelled by the same mixed guidance law identified previously, which produces a tail-chasing behavior that promotes implicit obstacle avoidance when led by a target that is itself avoiding clutter. When presented with obstacles blocking their path, hawks resolve the pursuit-avoidance conflict by applying a bias command that is well modelled as an open-loop steering correction aiming at a clearance of one wing length from an upcoming obstacle.