We present the results of a detailed analysis of galaxy properties along the red sequence in XMMU J1229+0151, an X-ray selected cluster at z = 0.98 drawn from the High Acuity Wide field K-band Imager Cluster Survey. Taking advantage of the broad photometric coverage and the availability of 77 spectra in the cluster field, we fit synthetic spectral energy distributions, and estimate stellar masses and photometric redshifts, which we use to determine the cluster membership. We investigate morphological and structural properties of red sequence galaxies and find that elliptical galaxies populate the bright end, while S0 galaxies represent the predominant population at intermediate luminosities, with their fraction decreasing at fainter magnitudes. A comparison with the low-redshift sample of the Wide Field Nearby Galaxy-clusters Survey cluster survey reveals that at z similar to 1 the bright end of the red sequence of XMMU J1229+0151 is richer in S0 galaxies. The faint end of the red sequence in XMMU J1229+0151 appears rich in disc-dominated galaxies, which are rarer in the low-redshift comparison sample at the same luminosities. Despite these differences between the morphological composition of the red sequence in XMMU J1229+0151 and in low-redshift samples, we find that to within the uncertainties, no such difference exists in the ratio of luminous to faint galaxies along the red sequence.