New nanocomposite material was prepared by high pressure processing of starting glass of nominal composition NaFePO$_{4}$. Thermal, structural, electrical and dielectric properties of the prepared samples were studied by differential thermal analysis (DTA), X-ray diffraction (XRD) and broadband dielectric spectroscopy (BDS). It was demonstrated that high pressure – high temperature treatment (HPHT) led to an increase of electrical conductivity of initial glasses by 2 orders of magnitude. It was also shown that the observed effect was stronger than for lithium analogue of this material studied by us earlier. The observed enhancement of conductivity was explained by Mott’s theory of electron hopping, which is more frequent in sample after pressure treatment. The final composite consisted of nanocrystalline NASICON and alluaudite phases, which are electrochemically active in potential cathode materials for Na batteries. Average dimensions of crystallites estimated from XRD studies were between 40 and 90 nm, depending on the phase. Some new aspects of local dielectric relaxations in studied materials were also discussed. It was shown that a combination of high pressures and BDS method is a powerful method to study relaxation processes and molecular movements in solids. It was also pointed out that high-pressure cathode materials may exhibit higher volumetric capacities compared with commercially used cathodes with carbon additions.