  We analyse the evolution of the red sequence in a sample of galaxy clusters
at redshifts $0.8<z<1.5$ taken from the HAWK-I Cluster Survey (HCS). The
comparison with the low-redshift ($0.04<z<0.08$) sample of the WIde-field
Nearby Galaxy-cluster Survey (WINGS) and other literature results shows that
the slope and intrinsic scatter of the cluster red sequence have undergone
little evolution since $z=1.5$. We find that the luminous-to-faint ratio and
the slope of the faint end of the luminosity distribution of the HCS red
sequence are consistent with those measured in WINGS, implying that there is no
deficit of red galaxies at magnitudes fainter than $M_V^*$ at high redshifts.
We find that the most massive HCS clusters host a population of bright red
sequence galaxies at $M_V < -22.0$ mag, which are not observed in low-mass
clusters. Interestingly, we also note the presence of a population of very
bright ($M_V < -23.0$ mag) and massive (${\log(M_*/M_\odot)} > 11.5$) red
sequence galaxies in the WINGS clusters, which do not include only the
brightest cluster galaxies and which are not present in the HCS clusters,
suggesting that they formed at epochs later than $z=0.8$. The comparison with
the luminosity distribution of a sample of passive red sequence galaxies drawn
from the COSMOS/UltraVISTA field in the photometric redshift range
$0.8<z_{phot}<1.5$ shows that the red sequence in clusters is more developed at
the faint end, suggesting that halo mass plays an important role in setting the
time-scales for the build-up of the red sequence.
