In this study, it is shown that in a layered nitride superconductor, i.e., ${\text{Li}}_{x}\text{ZrNCl}(0.07\ensuremath{\le}x\ensuremath{\le}0.21)$, the superconducting order parameter is highly anisotropic in a sample with $x=0.12$, as inferred from both the temperature and the magnetic field dependences of the muon depolarization rate (${\ensuremath{\sigma}}_{\text{s}}$, proportional to the superfluid density). Moreover, the tendency of strong anisotropy with an increase in $x$ is indicated by the $T$ dependence of ${\ensuremath{\sigma}}_{\text{s}}$. These observations are in good agreement with the recent theory that predicts the development of anisotropy in a $d+i{d}^{\ensuremath{'}}$ gap upon carrier filling to the bands with disconnected Fermi surfaces on a honeycomb lattice.