  The explicit breaking of chiral symmetry of the Wilson fermion action results
in additive quark mass renormalization. Moreover, flavour singlet and
non-singlet scalar currents acquire different renormalization constants with
respect to continuum regularization schemes. This complicates keeping the
renormalized strange quark mass fixed when varying the light quark mass in
simulations with $N_f=2+1$ sea quark flavours. Here we present and validate our
strategy within the CLS (Coordinated Lattice Simulations) effort to achieve
this in simulations with non-perturbatively order-$a$ improved Wilson fermions.
We also determine various combinations of renormalization constants and
improvement coefficients.
