Transmission lies at the interface of human immunodeficiency virus type 1 (HIV-1) evolution within and among hosts and separates distinct selective pressures that impose differences in both the mode of diversification and the tempo of evolution. In the absence of comprehensive direct comparative analyses of the evolutionary processes at different biological scales, our understanding of how fast within-host HIV-1 evolutionary rates translate to lower rates at the between host level remains incomplete. Here, we address this by analyzing pol and env data from a large HIV-1 subtype C transmission chain for which both the timing and the direction is known for most transmission events. To this purpose, we develop a new transmission model in a Bayesian genealogical inference framework and demonstrate how to constrain the viral evolutionary history to be compatible with the transmission history while simultaneously inferring the within-host evolutionary and population dynamics. We show that accommodating a transmission bottleneck affords the best fit our data, but the sparse within-host HIV-1 sampling prevents accurate quantification of the concomitant loss in genetic diversity. We draw inference under the transmission model to estimate HIV-1 evolutionary rates among epidemiologically-related patients and demonstrate that they lie in between fast intra-host rates and lower rates among epidemiologically unrelated individuals infected with HIV subtype C. Using a new molecular clock approach, we quantify and find support for a lower evolutionary rate along branches that accommodate a transmission event or branches that represent the entire backbone of transmitted lineages in our transmission history. Finally, we recover the rate differences at the different biological scales for both synonymous and non-synonymous substitution rates, which is only compatible with the 'store and retrieve' hypothesis positing that viruses stored early in latently infected cells preferentially transmit or establish new infections upon reactivation.