Anticipating and managing the impacts of sea-level rise for nations astride active tectonic margins requires rates of sea surface elevation change in relation to coastal land elevation to be understood. Vertical land motion (VLM) can either exacerbate or reduce sea-level changes with impacts varying significantly along a coastline. Determining rate, pattern, and variability of VLM near coasts leads to a direct improvement of location-specific relative sea level (RSL) estimates. Here, we utilise vertical velocity field from interferometric synthetic aperture radar (InSAR) data, calibrated with campaign and continuous Global Navigation Satellite System (GNSS), to determine the VLM for the entire coastline of New Zealand. Guided by existing knowledge of the seismic cycle, the VLM data infer long-term, interseismic rates of land surface deformation. We build probabilistic RSL projections using the Framework for Assessing Changes to Sea-level (FACTS) from IPCC Assessment Report 6 and ingest local VLM data to produce RSL projections at 7435 sites, thereby enhancing spatial coverage that was previously limited to tide gauges. We present ensembles of probability distributions of RSL for medium confidence climatic processes for each scenario to 2150 and low confidence processes to 2300. For regions where land subsidence is occurring at rates >2mm yr^-1 VLM makes a significant contribution to RSL projections for all scenarios out 2150. Beyond 2150, for higher emissions scenarios, the land ice contribution to global sea level dominates. We discuss the planning implications of RSL projections, where timing of threshold exceedance for coastal inundation can be brought forward by decades.