Frequency-dependent and temperature-dependent dielectric measurements are performed on double perovskite Tb$_2$NiMnO$_6$. The real ($epsilon_1$) and imaginary ($epsilon_2$) parts of dielectric permittivity show three plateaus suggesting dielectric relaxation originating from bulk, grain boundaries and the sample-electrode interfaces respectively. The temperature and frequency variation of $epsilon_1$ and $epsilon_2$ are successfully simulated by a $RC$ circuit model. The complex plane of impedance, $Z$-$Z$, is simulated using a series network with a resistor $R$ and a constant phase element. Through the analysis of frequency-dependent dielectric constant using modified-Debye model, different relaxation regimes are identified. Temperature dependence of dc conductivity also presents a clear change in slope at, $T^*$. Interestingly, $T^*$ compares with the temperature at which an anomaly occurs in the phonon modes and the Griffiths temperature for this compound. The components $R$ and $C$ corresponding to the bulk and the parameter $alpha$ from modified-Debye fit tend support to this hypothesis. Though these results cannot be interpreted as magnetoelectric coupling, the relationship between lattice and magnetism is marked.
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