A dielectric is an insulating material that increases capacitance when placed between capacitor plates. Dielectric constant K = C_with/C_without >= 1. Two scenarios must be distinguished:

Battery connected (V constant): Inserting dielectric increases C by K. Since V is fixed, Q = CV increases by K. E = V/d stays the same. Energy U = (1/2)CV^2 increases by K. Extra energy comes from the battery.

Battery disconnected (Q constant): C increases by K. V = Q/C decreases by K. E = V/d decreases by K. Energy U = Q^2/(2C) decreases by K. Lost energy goes into pulling the dielectric in (or is released as work).

The dielectric is pulled into the capacitor in both cases — this is because the system moves toward lower energy (battery off) or the battery supplies energy to increase the charge (battery on). Force on dielectric slab (partially inserted, battery on): F = (1/2)*(K-1)epsilon_0(A/d)*V^2 / L, where L is the plate length.