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Reactivation of pre‐existing intra‐basement structures can influence the evolution of rift basins, yet the detailed kinematic relationship between these structures and overlying rift‐related faults remains poorly understood. Understanding the kinematic as well as geometric relationship between intra‐basement structures and rift‐related fault networks is important, with the extension direction in many rifted provinces typically thought to lie normal to fault strike. We here investigate this problem using a borehole‐constrained, 3D seismic reflection dataset from the Taranaki Basin, offshore New Zealand. Excellent imaging of intra‐basement structures and a relatively weakly deformed, stratigraphically simple sedimentary cover allow us to: (a) identify a range of interaction styles between intra‐basement structures and overlying, Plio‐Pleistocene rift‐related normal faults; and (b) examine the cover fault kinematics associated with each interaction style. Some of the normal faults parallel and are physically connected to intra‐basement reflections, which are interpreted as mylonitic reverse faults formed during Mesozoic subduction and basement terrane accretion. These geometric relationships indicate pre‐existing intra‐basement structures locally controlled the position and attitude of Plio‐Pleistocene rift‐related normal faults. However, through detailed 3D kinematic analysis of selected normal faults, we show that: (a) normal faults only nucleated above intra‐basement structures that experienced late Miocene compressional reactivation, (b) despite playing an important role during subsequent rifting, intra‐basement structures have not been significantly extensionally reactivated, and (c) preferential nucleation and propagation of normal faults within late Miocene reverse faults and folds appears to be the key genetic relationship between contractionally reactivated intra‐basement structures and rift‐related normal faults. Our analysis shows that km‐scale, intra‐basement structures can control the nucleation and development of newly formed, rift‐related normal faults, most likely due to a local perturbation of the regional stress field. Because of this, simply inverting fault strike for causal extension direction may be incorrect, especially in provinces where pre‐existing, intra‐basement structures occur. We also show that a detailed kinematic analysis is key to deciphering the temporal as well as simply the spatial or geometric relationship between structures developed at multiple structural levels. [ABSTRACT FROM AUTHOR]