  We propose a form of gravity-matter interaction given by $\omega RT$ in the
framework of $f(R,T)$ gravity and examine the effect of such interaction in
spherically symmetric compact stars. Treating the gravity-matter coupling as a
perturbative term on the background of Starobinsky gravity, we develop a
perturbation theory for equilibrium configurations. For illustration, we take
the case of quark stars and explore their various stellar properties. We find
that the gravity-matter coupling causes an increase in the stable maximal mass
which is relevant for recent observations on binary pulsars.
