The biological role of the repetitive DNA sequences in the human genome remains an outstanding question. Recent long-read human genome assemblies have allowed us to identify a function for one of these repetitive regions. We have uncovered a tandem array of conserved primate-specific retrogenes encoding the protein Elongin A3 (ELOA3), a homolog of the RNA polymerase II (RNAPII) elongation factor Elongin A (ELOA). Our genomic analysis shows that the ELOA3 gene cluster is conserved among primates and the number of ELOA3 gene repeats is variable in the human population and across primate species. Moreover, the gene cluster has undergone concerted evolution and homogenization within primates. Our biochemical studies show that ELOA3 functions as a promoter-associated RNAPII pause-release elongation factor with distinct biochemical and functional features from its ancestral homolog, ELOA. We propose that the ELOA3 gene cluster has evolved to fulfil a transcriptional regulatory function unique to the primate lineage that can be targeted to regulate cellular hyperproliferation.