The displacement current flows in the dielectric of a capacitor when the potential difference across its plates

is increasing with time

According to Maxwell's hypothesis, a displacement current will flow through a capacitor when the potential difference across its plates is varying. Thus a varying electric field will exist between the plates and this displacement current is same in magnitude to the current flowing in outer circuit.  When a D.C voltage applied across its plates, constant voltage appears across its plates and so there will be no displacement current flowing through the capacitor. Thus the displacement current will flow when the potential is increasing with time.