The reactivity and selectivity of bimetallic surfaces are of fundamental importance in industrial applications. Here, we report the first six-dimensional (6D) quantum dynamics study for the role of surface strain and ligand effects on the reactivity of HCl on a strained pseudomorphic monolayer of Au deposited onto a Ag(111) substrate, with the aid of accurate machine learning-based potential energy surfaces. The substitute of Au into Ag changes the location of the transition state; however, the static barrier height remains roughly the same as pure Au(111). The 6D quantum dynamics calculations reveal that the surface strain due to lattice expansion slightly enhances the reactivity. The ligand effect due to electronic structure interactions between Au and Ag substantially suppresses the reactivity of HCl in the ground vibrational state but promotes the reactivity via vibrational excitation at high kinetic energies. This finding can be attributed to more close interaction with Ag atoms at the transition state close to the fcc site, as well as the tight transition-state region, making the vibrational excitation highly efficient in enhancing the reactivity. Our study quantitatively unravels the dynamical origin of reactivity control by two metals, which will ultimately provide valuable insight into the selectivity of the catalyst.