The molecular level understanding of ion and polymer dynamics in nanoparticle-coupled hydrogel network polymer electrolytes is investigated by linear dielectric and viscoelastic measurements covering broad ranges of frequency and temperature. We prepare hydrogel polymer electrolytes (HPEs), composed of Li+ conducting hydrophilic poly(lithium acrylate) (PLiA) as the HPE matrix and vinyl-functionalized silica nanoparticles (NPs) as cross-linking points, via radical polymerization and sol–gel reaction. The NP content variation leads to changes in ionic conductivity (σDC), dielectric constant (εs), relaxation frequency, and elastic modulus, which are important characteristic factors for understanding ion transport. From the physical model of electrode polarization (EP), allowing for the determination of the number density of simultaneously conducting ions and their mobility, the NP-containing HPEs (HPE-NP) have simultaneously higher conducting ion concentration (p) and mobility (μ), resulting in higher ionic conductivity (σDC ∼ pμ), compared to the HPE without NPs. The temperature dependence of p and μ follows Arrhenius (thermally activated) and Vogel–Fulcher (segmentally driven) temperature dependences, respectively. In addition to the lower frequency EP, the HPEs show higher frequency relaxation (α2), attributed to ions rearranging. NP incorporation leads to faster α2 relaxation and higher static dielectric constant εs (shorter Bjerrum length lB). Time–temperature superposition (tTS) works well for these electrolytes and is applied to construct master curves of viscoelasticity and in-phase conductivity. In the end, the NP-containing HPE-based supercapacitor is fabricated using carbon nanotube yarn (CNTY) electrodes and shows stable electrochemical performance, demonstrating that our HPE can be a solid-state polymer electrolyte for energy storage devices.