[en] This work is devoted to the investigation of new holographic dark energy (infrared cutoff is the Hubble radius) in locally rotationally symmetric Bianchi type-$I$ universe within the framework of Saez–Ballester (Phys. Lett. A 113:467, 1986) scalar–tensor theory of gravitation. We construct interacting and non-interacting dark energy models by solving the field equations using a relationship between the metric potentials. This leads to a variable deceleration parameter model which exhibits a transition of the universe from deceleration to acceleration. We evaluate various cosmological parameters of our models. We have observed that the energy density parameters, equation of state and important cosmological planes (${\mathrm{\omega <!--\; ??\; -->}}_{\mathit{d}\mathit{e}}-<!--\; ???\; -->{\mathrm{\omega <!--\; ??\; -->}}_{\mathit{d}\mathit{e}}^{\prime }$ and $r-<!--\; ???\; -->s$) yield the results compatible with the modern observational data. We have, also, discussed the stability analysis of our models.