Deviations of the measured LFU ratios such as $R_{D^{(*)}}$ and $R_{J/\psi}$ from the standard model predictions by 3.3 $\sigma$ and 1.8 $\sigma$, respectively, indicate the possible existence of new physics beyond the standard model. Precise measurements of other observables in decays involving $b\to c \ell \nu_\ell$ transitions in the future may substantiate or rule out the presence of new physics. Hence, it becomes important to analyze complementary $b\to c \ell \nu_\ell$ channels also, such as $B_s\to D_s^{**}\ell\nu_\ell$, where $D_s^{**} = \{D_{s0}^*, D_{s1}^*, D_{s1}, D_{s2}^*\}$. The measured ratios $R_{D^{(*)}}$ suggest an excess of taus, whereas the measured ratio $R_{\Lambda_c}$ shows a deficit in taus. The complementary information obtained from the measurement of LFU ratios like $R_{D_s^{**}}$ may become crucial in the interpretation of the contributing new physics. In this work, we analyze various $q^2$-dependent observables pertaining to the $B_s\to D_s^{**}\ell\nu_\ell$ decay modes within a new physics approach. The new interactions are constrained using available experimental data of $b\to c \ell \nu_\ell$ transitions.