  We study an isotropic flat FLRW-model in Scale-covariant theory of gravity $
f_{\gamma \delta}(\phi) $ \cite{Canuto:1977zz} which is explained in terms of
ordinary and covariant differentiation of scalar field $ \phi $. As we know the
deceleration parameter is time-dependent, so we consider the deceleration
parameter $ q $ as the function of $ t $. Using this methodology, we find all
the important cosmological factors in terms of a hyperbolic function of the
cosmic time $ t $. In turn, we create the model having the behavior of the
late-time universe, which is ever accelerated expanding and faces a Big Freeze
at the end. The model shows the quintessence dark energy model from early to
late times. We compute the constrained values of Hubble parameter $
H_0=70.979^{+0.021}_{-0.0043} $ and the model parameter $
n=1.24079^{+0.00015}_{-0.00079} $ using joint analysis of the $ OHD $ data of
77-points and Pantheon bin data. The model exhibits point-type singularity,
beginning with a point of zero volume, infinite energy density, and
temperature. Furthermore, we obtain the present deceleration parameter $ (q_0)
\approx {-0.54} $. Also, we examine the ultimate behavior of our model by
properly analyzing energy conditions, cosmographical parameters, and
Statefinder diagnostic. Finally, the proposed model behaves like a quintessence
dark energy model.
