The aim of our investigation is to derive a particular theory among the class
of scalar-tensor(ST) theories of gravity, and then to test it by studying
kinematics and dynamics of S-stars around a supermassive black hole (BH) at
Galactic Center (GC). We also discuss the Newtonian limit of this class of
ST theories of gravity, as well as its parameters. We compare the observed
orbit of S2 star with our simulated orbit which we obtained theoretically
with the derived ST potential and constrained parameters. Using the obtained
best-fit parameters we calculated orbital precession of S2 star in ST
gravity and found that it has the same direction as in General Relativity
(GR) but causes much larger pericenter shift.