  In light of the statistical performance of cosmological observations, in this
work we present an improvement on the Gaussian reconstruction of the Hubble
parameter data $H(z)$ from Cosmic Chronometers, Supernovae Type Ia and
Clustering Galaxies in a model-independent way in order to use them to study
new constraints in the Horndeski theory of gravity. First, we have found that
the prior used to calibrate the Pantheon supernovae data significantly affects
the reconstructions, leading to a 13-$\sigma $ tension on the $H_0$ value.
Second, according to the $\chi^{2}$-statistics, the reconstruction carried out
by the Pantheon data calibrated using the $H_{0} $ value measured by The
Carnegie-Chicago Hubble Program is the reconstruction which fits best the
observations of Cosmic Chronometers and Clustering of Galaxies datasets.
Finally, we use our reconstructions of $H(z)$ to impose model-independent
constraints in general cosmological viable Horndeski models, landscape in where
we found that a Horndeski model that represents an extension to Quintessence
can reproduce the reconstructions of the late expansion of the universe within
2-$\sigma$.
