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In this work, a new law of a varying deceleration parameter of a third degree has been proposed. The solutions of the modified field equations have been derived under the newly proposed law of the deceleration parameter. The model exhibits the big bang singularity at a cosmic time (t = 0) and shows a big rip at t = n, and then, it reenters the phase of initial singularity at t = 2n and ends its cyclic behavior at t = 3n. The evolution of the physical and dynamical parameters of the Universe has been studied, and the graphical representation has also been shown. Further, Om(z) diagnostic parameter and the energy conditions have also been studied together with their graphical representations.