To study the influence of a polymeric substrate, hydroxypropylcellulose (HPC), on the dynamics of the nematic mixture E7, the real (ε′) and imaginary (ε″) parts of the complex dielectric permittivity of the unaligned composite system (polymeric substrate covered with liquid crystal) were measured as a function of frequency and temperature, and compared with those of unaligned pure E7. The temperature range was extended down to the supercooled region. Three superimposed processes were detected, related to different alignment states in relation to the electric field: (1) a main relaxation mechanism due to the hindered rotation of molecules about their short axis, corresponding to the case where the director is parallel to the electric field in an oriented sample, (2) a low frequency process attributed to molecular aggregates, and (3) a high frequency process due to the tumbling of molecules. Processes (2) and (3) correspond to the case when the director is perpendicular to the electric field in an oriented sample. In the composite system the main relaxation mechanism results in a faster process but the other two processes almost superimpose in the frequency window, the high frequency process being much more intense relative to pure E7. The enhancement of the high frequency process in HPC + E7 can be interpreted as an increase in the number of dipoles whose director has a component aligned perpendicular to the electric field, due to surface effects. The temperature dependence of the main and high frequency relaxation mechanisms obeys the VFT law, which is a feature of glass-like systems.