To improve ZnO dispersion in your polymer electrolyte, try surface modifying ZnO with surfactants or coupling agents and use stronger probe sonication or mixed solvents. Also, optimize nanoparticle concentration and combine sonication with mechanical stirring for better results.

Increasing intensity of sonication is not the solution as such. The particle surface has to be (made) compatible with the polymer electrolyte and solvent if used. Not only successful dispersion but also high kinetic stability is necessary.

Without surfactant? Impossible

You might try high pressure homogenization, so you have more control on complete treatment (sonication might apply different energy in different area of the bath) and on temperature as nmp has a relatively low Cp and raises quicky its temperature.