We present here a characterization of the low background NaI(Tl) crystal NaI-33 based on a period of almost one year of data taking (891 kg × days exposure) in a detector configuration with no use of organic scintillator veto. This remarkably radio-pure crystal already showed a low background in the SABRE Proof-of-Principle (PoP) detector, in the low energy region of interest (1–6 keV) for the search of dark matter interaction via the annual modulation signature. As the vetoable background components, such as 40 K, are here sub-dominant, we reassembled the PoP setup with a fully passive shielding. We upgraded the selection of events based on a Boosted Decision Tree algorithm that rejects most of the PMT-induced noise while retaining scintillation signals with > 90% efficiency in 1–6 keV. We find an average background of 1.39 ± 0.02 counts/day/kg/keV in the region of interest and a spectrum consistent with data previously acquired in the PoP setup, where the external veto background suppression was in place. Our background model indicates that the dominant background component is due to decays of 210 Pb, only partly residing in the crystal itself. The other location of 210 Pb is the reflector foil that wraps the crystal. We now proceed to design the experimental setup for the physics phase of the SABRE North detector, based on an array of similar crystals, using a low radioactivity PTFE reflector and further improving the passive shielding strategy, in compliance with the new safety and environmental requirements of Laboratori Nazionali del Gran Sasso.