Sodium batteries are an attractive alternative for future energy storage as they can be produced with abundant and low-cost materials. Nonetheless, sodium-ion batteries (SIBs) are often composed of flammable and volatile carbonate-based liquid electrolytes. Polymer electrolytes have attracted significant attention as safer alternatives. Among polymer electrolytes, single-ion conductive polymer electrolytes (SIPEs) are considered particularly interesting because they can suppress dendrite growth, enabling high-performance (quasi)-solid-state sodium–(metal) batteries. In this work, a self-standing, flexible, quasi-solid-state SIPE is investigated, which is composed of sodium 4-styrene sulfonyl (trifluoromethanesulfonyl) imide (NaSTFSI), pentaerythritol tetrakis(3-mercaptopropionate) (PETMP) and pentaerythritol tetraacrylate (PET4A) blended with poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP). The SIPE membrane, including 50 wt% of molecular transporter, exhibits ionic conductivity of 1.4 × 10$^{−5}$ S cm$^{−1}$ and 1.3 × 10$^{−4}$ S cm$^{−1}$ at 20 °C and 90 °C, respectively, thermal stability up to 280 °C, electrochemical stability window up to 4.5 V vs. Na/Na$^+$, and Na plating/stripping reversibility in symmetric Na‖Na cells. The manufactured SIPE implemented in Prussian White (PW)‖Na cells enables the delivery of 147 mA h g$^{−1}$ of PW at 15 mA g$^{−1}$ with a Coulombic efficiency of over 99%, which is comparable with the PW‖Na cells using liquid carbonate electrolyte, confirming the suitability of the designed SIPE for sodium–(metal) batteries.