Modelling a capacitor whose dielectric has resistance as a circuit element
It seems you are asking how to more simply model a capacitor with "leaky" dielectric.  The answer is a ideal capacitor with a resistor in parallel.

Charge up the capacitor to a fixed voltage and wait.  The real capacitor will discharge slowly because of the finite resistance of the dielectric.  The simplified model exhibits the same discharge due to the resistance across the ideal capacitor.

With a steady voltage applied externally, both also result in the same current, which is the voltage divided by the leakage resistance.

In general, the first order approximation of a capacitor is simply a ideal capacitor.  For many uses of real capacitors, this is good enough.

The second approximation has a resistor both in series with a ideal capacitor, and one in parallel with it.  The series resistance is referred to as the ESR (equivalent series resistance).  This can matter in real circuits, especially when the cap is subjected to high currents.

The parallel resistance models the leakage inherent in the dielectric.  This is so little (resistance so high) in ceramic capacitors that it can usually be ignored.  However, leakage is more significant in other types, like electrolytic, and must be taken into account in some applications.

Note that both the equivalent series and leakage resistances can vary significantly over temperature.  The leakage of electrolytic caps in particular go up significantly with higher temperature.

Of course these are all models with different tradeoffs between simplicity and fidelity.  You can get really anal and make a model of a capacitor that takes into account all kinds of third order effects, like series inductance, distributed capacitance between the series inductors, between the multiple distributed series and parallel resistances, their inductance, etc, etc, etc.  The more you keep going, the more you model the true behavior of any one capacitor, but the less practical the model is for designing circuits.