A dielectric is an insulating material that increases capacitance when placed between capacitor plates. Dielectric constant K = $\frac{C_with}{C_without}$ >= 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 = $\frac{V}{d}$ stays the same. Energy U = \frac{1}{2}$$CV^2 increases by K. Extra energy comes from the battery.

Battery disconnected (Q constant): C increases by K. V = $\frac{Q}{C}$ decreases by K. E = $\frac{V}{d}$ decreases by K. Energy U = Q^$\frac{2}{2C}$ 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 = $\frac{1}{2}$(K-1)$epsilon_0$$\frac{A}{d}$$V^2$ / L, where L is the plate length.