  We consider possible signatures for the so called {\it hybrid gravity} within
the Galactic Central Parsec. This modified theory of gravity consists of a
superposition of the metric Einstein-Hilbert Lagrangian with an $f(R)$ term
constructed {\it \`{a} la Palatini} and can be easily reduced to an equivalent
scalar-tensor theory. Such an approach is introduced in order to cure the
shortcomings related to $f(R)$ gravity, in general formulated either in metric
or in metric-affine frameworks. Hybrid gravity allows to disentangle the
further gravitational degrees of freedom with respect to those of standard
General Relativity. The present analysis is based on the S2 star orbital
precession around the massive compact dark object at the Galactic Centre where
the simulated orbits in hybrid modified gravity are compared with astronomical
observations. These simulations result with constraints on the range of hybrid
gravity interaction parameter $\phi_0$, showing that in the case of S2 star it
is between -0.0009 and -0.0002. At the same time, we are also able to obtain
the constraints on the effective mass parameter $m_{\phi}$, and found that it
is between -0.0034 and -0.0025 AU$^{-1}$ for S2 star. Furthermore, the hybrid
gravity potential induces precession of S2 star orbit in the same direction as
General Relativity. In previous papers, we considered other types of extended
gravities, like metric power law $f(R)\propto R^n$ gravity, inducing Yukawa and
Sanders-like gravitational potentials, but it seems that hybrid gravity is the
best among these models to explain different gravitational phenomena at
different astronomical scales.
