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At this time, the development of advanced elastic dielectric materials for use in organic devices, particularly in organic field-effect transistors, is of considerable interest to the scientific community. In the present work, flexible poly(dimethylsiloxane) (PDMS) specimens cross-linked by means of ZnCl2-bipyridine coordination with an addition of 0.001 wt. %, 0.0025 wt. %, 0.005 wt. %, 0.04 wt. %, 0.2 wt. %, and 0.4 wt. % of gold nanoparticles (AuNPs) were prepared in order to understand the effect of AuNPs on the electrical properties of the composite materials formed. The broadband dielectric spectroscopy measurements revealed one order of magnitude decrease in loss tangent, compared to the coordinated system, upon an introduction of 0.001 wt. % of AuNPs into the polymeric matrix. An introduction of AuNPs causes damping of conductivity within the low-temperature range investigated. These effects can be explained as a result of trapping the Cl− counter ions by the nanoparticles. The study has shown that even a very low concentration of AuNPs (0.001 wt. %) still brings about effective trapping of Cl− counter anions, therefore improving the dielectric properties of the investigated systems. The modification proposed reveals new perspectives for using AuNPs in polymers cross-linked by metal-ligand coordination systems.