  We determine the non-perturbatively renormalized axial current for O($a$)
improved lattice QCD with Wilson quarks. Our strategy is based on the chirally
rotated Schr\"odinger functional and can be generalized to other finite (ratios
of) renormalization constants which are traditionally obtained by imposing
continuum chiral Ward identities as normalization conditions. Compared to the
latter we achieve an error reduction up to one order of magnitude. Our results
have already enabled the setting of the scale for the $N_{\rm f}=2+1$ CLS
ensembles [1] and are thus an essential ingredient for the recent $\alpha_s$
determination by the ALPHA collaboration [2]. In this paper we shortly review
the strategy and present our results for both $N_{\rm f}=2$ and $N_{\rm f}=3$
lattice QCD, where we match the $\beta$-values of the CLS gauge configurations.
In addition to the axial current renormalization, we also present precise
results for the renormalized local vector current.
