  We study the renormalization group evolution (RGE) of new physics
contributions to (semi)leptonic charged-current meson decays, focusing on
operators involving a chirality flip at the quark level. We calculate their
evolution under electroweak and electromagnetic interactions, including also
the three-loop QCD running and provide numerical formulas that allow us to
connect the values of the corresponding Wilson coefficients from scales at the
TeV to the low-energy scales. The large mixing of the tensor operator into the
(pseudo)scalar ones has important phenomenological implications, such as the
RGE of new physics bounds obtained from light quark decays or in $b\to
c\ell\nu$ transitions. For instance, we study scenarios involving tensor
effective operators, which have been proposed in the literature to address the
$B$-decay anomalies, most notably those concerning the $R_{D^{(*)}}$ ratios. We
conclude that the loop effects are important and should be taken into account
in the analysis of these processes, especially if the operators are generated
at an energy scale of $\sim 1$ TeV or higher.
