  We are studying the mechanism of the cosmic model in the presence of GGPDE
and matter in LRS Bianchi type-I space-time by the utilization of new
holographic DE in Saez-Ballester theory. Here we discuss all the data for three
scenarios, first is supernovae type Ia union data, second is SN Ia data in
combination with BAO and CMB observations and third is combination with OHD and
JLA observations. From this, we get a model of our universe, where its transit
state from deceleration to acceleration phase. Here we have observed that the
results yielded by cosmological parameters like $\rho$ (energy density), EoS
(equation of state), squared speed of sound $(v_s^2)$,
$(\omega_D-\omega_D^{'})$ and $(r-s)$ plane is compatible with the recent
observational data. The $(\omega_D-\omega_D^{'})$ trajectories in both thawing
and freezing regions and the correspondence of the quintessence field with GGPD
dark energy are discussed. Some physical aspects of the GGPDE models are also
highlighted.
