  In this paper, we examine the (LRS) Bianchi-type-I cosmological model with
holographic dark energy. The exact solutions to the corresponding field
equations are obtained by using generalized hybrid expansion law (HEL). The EoS
parameter $\omega$ for DE is found to be time dependent and redshift dependent
and its exiting range for derived model is agreeing well with the current
observations. Here we likewise apply two mathematical diagnostics, the
statefinder ({r, s}) and $\omega_{d}-\omega^{'}_{d}$ plane to segregate HDE
model from the $\Lambda CDM$ model. Here the $\omega_{d}-\omega^{'}_{d}$
diagnostic trajectories is the good tool to classifying the dynamical DE model.
We found that our model lies in both thawing region and freezing region. We
have also construct the potential as well as dynamics of the quintessence and
tachyon scalar field. Some physical and geometric properties of this model
along with the physical acceptability of cosmological solution have been
discussed in detail.
