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Motivated by the persistent anomalies in the semileptonic $B$-meson decays,we investigate the competency of LHC data to constrain the$R_{D^{(*)}}$-favoured parameter space in a charge $-1/3$ scalar leptoquark($\mathcal S_1$) model. We consider some scenarios with one large free couplingto accommodate the $R_{D^{(*)}}$ anomalies. As a result, some of themdominantly yield nonresonant $\tau\tau$ and $\tau\nu$ events at the LHC throughthe $t$-channel $\mathcal S_1$ exchange. So far, no experiment has searched forleptoquarks using these signatures and the relevant resonant leptoquarksearches are yet to put any strong exclusion limit on the parameter space. Werecast the latest $\tau\tau$ and $\tau\nu$ resonance search data to obtain newexclusion limits. The nonresonant processes strongly interfere (destructivelyin our case) with the Standard Model background and play the determining rolein setting the exclusion limits. To obtain precise limits, we includenon-negligible effects coming from the subdominant (resonant) pair andinclusive single leptoquark productions systematically in our analysis. To dealwith large destructive interference, we make use of the transverse massdistributions from the experiments in our statistical analysis. In addition, wealso recast the relevant direct search results to obtain the most stringentcollider bounds on these scenarios to date. These are independent bounds andare competitive to other known bounds. Finally, we indicate how one can adoptthese bounds to a wide class of models with $\mathcal S_1$ that are proposed toaccommodate the $R_{D^{(*)}}$ anomalies.

$R_{D^{(*)}}$ motivated $\mathcal{S}_1$ leptoquark scenarios: Impact of interference on the exclusion limits from LHC data