  We present theoretical calculations of the optical spectrum of monolayer
MoS$_2$ with a charged defect. In particular, we solve the Bethe-Salpeter
equation based on an atomistic tight-binding model of the MoS$_2$ electronic
structure which allows calculations for large supercells. The defect is
modelled as a point charge whose potential is screened by the MoS$_2$
electrons. We find that the defect gives rise to new peaks in the optical
spectrum approximately 100-200 meV below the first free exciton peak. These
peaks arise from transitions involving in-gap bound states induced by the
charged defect. Our findings are in good agreement with experimental
measurements.
