A localized turbulent region expands spatially by entraining surrounding non-turbulent fluid, demarcated by the turbulent/non-turbulent interface (TNTI) layer. Small-scale vortex tubes and shear layers within this TNTI layer play a pivotal role in the process of entrainment. Shear layers in turbulence are known to be unstable against perturbations with wavelengths approximately 30 times the Kolmogorov scale. This study conducts numerical experiments aimed at investigating the potential for enhancing passive scalar mixing through the excitation of small-scale shear instability. Direct numerical simulations (DNS) are conducted for a turbulent front with a passive scalar transfer evolving in the absence of mean shear, where solenoidal velocity perturbations of constant wavelength are introduced outside the turbulent region. These perturbations are found to enhance the entrainment rate significantly when their wavelength coincides with the unstable mode of shear layers. Despite the increased entrainment rate facilitated by the excitation of small-scale shear instability, passive scalar statistics dominated by large-scale scalar distributions, such as mean scalar and root-mean-squared scalar fluctuations, remain largely unaffected. However, this enhanced entrainment rate results in the amplification of the scalar dissipation rate, which provides a measure of scalar mixing at small scales. These findings indicate that exciting small-scale shear instability can effectively enhance entrainment and small-scale scalar mixing in intermittent turbulent flows.