We present electrical resistivity measurements on the prototypical heavy-fermion metal YbRh$_{2}$Si$_{2}$ (YRS) under $a$-axis tensile and compressive strain and focus on the evolution of the resistivity maximum near 136~K that arises from the interplay of the Kondo effect and the crystal electric field (CEF) splitting. While compressive strain reduces $T_{\rm max}$, similar as previously reported for hydrostatic pressure, $T_{\rm max}$ is enhanced up to 145~K for 0.13\% tensile strain. Model calculations for the strain effect on CEF splitting in YRS reveal a negligible shift of the levels. Instead, the enhancement of the resistivity maximum indicates a 20\% increase of the Kondo temperature. This opens the perspective to access the hidden zero-field QCP in pure YRS.