  The current analysis uses the non-static plane symmetric space-time to
dynamically examine the holographic dark energy model as a candidates of IR
cut-offs (specifically Hubble's and Granda-Oliveros cut-off). Using the Markov
Chain Monte Carlo (MCMC) method, we estimate the best fit values for the model
parameters imposed from the combined datasets of $CC+SC+BAO$. Now, it has been
found that the characteristics of space-time that have been addressed and
formulated using both models are flat universe and observed that the model
appears to be in good agreement with the observations. In addition, we
investigate the behavior of equation of state parameters along with the energy
conditions. Finally, we found that in both the cut-offs the models predict that
the present and late universe are accelerating and the equation of state
parameter behaves like the quintessence model.
