We use the Illustris-TNG simulations to explore the dynamic scaling relation between massive clusters and their central galaxies (BCGs). The Illustris TNG300-1 simulation we use includes 280 massive clusters with M 200 > 10 14 M enabling a robust statistical analysis. We derive the line-of-sight velocity dispersion of the stellar particles of the BCGs (σ * ,BCG ), analogous to the observed BCG stellar velocity dispersion. We also compute the subhalo velocity dispersion to measure the cluster velocity dispersion (σ cl ). Both σ * ,BCG and σ cl are proportional to the cluster halo mass, but the slopes differ slightly. Thus like the observed relation, σ * ,BCG /σ cl declines as a function of σ cl , but the scatter is large. We explore the redshift evolution of σ * ,BCG − σ cl scaling relation for z 1 in a way that can be compared directly with observations. The scaling relation has a similar slope at high redshift, but the scatter increases because of the large scatter in σ * ,BCG . The simulations imply that high redshift BCGs are dynamically more complex than their low redshift counterparts.