  A new parametrization of the Hubble parameter is proposed to explore the
issue of the cosmological landscape. The constraints on model parameters are
derived through the Markov Chain Monte Carlo (MCMC) method by employing a
comprehensive union of datasets such as 34 data points from cosmic chronometers
(CC), 42 points from baryonic acoustic oscillations (BAO), a recently updated
set of 1701 Pantheon$^+$ (P22) data points derived from Type Ia supernovae
(SNeIa), and 162 data points from gamma-ray bursts (GRBs). Furthermore, the
models are compared by using the Akaike Information Criterion (AIC) and
Bayesian Information Criterion (BIC), so that a comparative assessment of model
performance can be available. Additionally, we compare the Dainotti relation
via Gaussian likelihood analysis versus new likelihoods and Calibration of the
Dainotti relation through a model-independent method. The kinematic behavior of
the models is also investigated by encompassing the transition from
deceleration to acceleration and the evolution of the jerk parameter. From the
analysis of the parametric models, it is strongly indicated that the Universe
is currently undergoing an accelerated phase with diagnostics of the model
validating the quintessence phase.
