The role of biotic interactions, such as interspecific competition, in driving geographical range evolution is still poorly understood. For instance, lineages distributed across regions with a large number of potential competitors might experience some level of geographical packing of their range limits, so that changes in their geographical distributions are hampered. Conversely, a large number of competitors could instead lead to accelerated rates of geographical range evolution, with lineages shifting their ranges to avoid competition. We recently introduced the concept of clade density (CD; the sum of the areas of overlap between a species and other members of its higher taxon, weighted by their phylogenetic distance) as a proxy of the potential for interspecific competition across the geographical distribution of a given species. In this study, we used a large dataset with 5936 terrestrial vertebrate species to test whether CD is significantly associated with variation in the rate of geographical range evolution using two alternative approaches. First, we tested if there is a significant relationship between CD and the geographical distance between sister species. In addition, we estimated tip rates of geographical range evolution and tested if they were consistently associated with variation in CD. We found no evidence for an effect of CD on geographical range evolution in either of the tested approaches, even after accounting for phylogenetic uncertainty. These results are inconsistent with equilibrial models of species diversification and suggest that interspecific competition might not play a pervasive role in geographical range evolution of terrestrial vertebrates.