We present new spectroscopic observations in a field containing the highest redshift cluster of the ESO Distant Cluster Survey (EDisCS). We measure galaxy redshifts and determine the velocity dispersions of the galaxy structures located in this field. Together with the main cluster Cl 1103.7-1245 (z = 0.9580; sigma(clus) = 522 +/- 111 km s(-1)) we find a secondary structure at z = 0.9830, Cl 1103.7-1245c. We then characterize the galaxy properties in both systems, and find that they contain very different galaxy populations. The cluster Cl 1103.7-1245 hosts a mixture of passive elliptical galaxies and star-forming spirals and irregulars. In the secondary structure Cl 1103.7-1245c all galaxies are lower-mass star-forming irregulars and peculiars. In addition, we compare the galaxy populations in the Cl 1103.7-1245 z = 0.9580 cluster with those in lower redshift EDisCS clusters with similar velocity dispersions. We find that the properties of the galaxies in Cl 1103.7-1245 follow the evolutionary trends found at lower redshifts: the number of cluster members increases with time in line with the expected growth in cluster mass, and the fraction of passive early-type galaxies increases with time while star-forming late types become less dominant. Finally, we find that the mean stellar masses are similar in all clusters, suggesting that massive cluster galaxies were already present at z similar to 1.