The decays governed by the flavor-changing-neutral-current transitions (FCNC), such as b โ sโ+โโ, provide an important tool to test the physics in and beyond the Standard Model (SM). This work focuses on investigating the FCNC process $B_{c}\rightarrow D_{s}^{*} \left(\rightarrow D_{s}\pi \right)\ell ^{+}\ell ^{-}(\ell =e,\mu ,\tau )$. Being an exclusive process, the initial and final state meson matrix elements involve the form factors, which are non-perturbative quantities and need to be calculated using specific models. By using the form factors calculated in the covariant light-front quark model, we analyze the branching fractions and angular observables such as the forward-backward asymmetry AFB, polarization fractions (Longitudinal and transverse) FL(T), CP asymmetry coefficients Ai and CP-averaged angular coefficients Si, both in the SM and some new physics (NP) scenarios. Some of these physical observables are a potential source of finding the physics beyond the SM and help us distinguish various NP scenarios.