  We analyze the post-Newtonian orbit of stars around a deformed Kerr black
hole. The deformation we consider is a class of disformal transformations of a
nontrivial Kerr solution in scalar-tensor theory which are labeled via the
disformal parameter $D$. We study different limits of the disformal parameter,
and compare the trajectories of stars orbiting a black hole to the case of the
Kerr spacetime in general relativity, up to 2PN order. Our findings show that
for generic nonzero $D$, the no-hair theorem of general relativity is violated,
in the sense that the black hole's quadrupole $Q$ is not determined by its mass
$M$ and angular momentum $J$ through the relation $Q=-J^2/M$. Limiting values
of $D$ provide examples of simple and exact noncircular metric solutions,
whereas in a particular limit, where $1+D$ is small but finite, we obtain a
leading correction to the Schwarzschild precession due to disformality. In this
case, the disformal parameter is constrained using the recent measurement of
the pericenter precession of the star S2 by the GRAVITY Collaboration.
