How evolutionary changes at enhancers affect the transcription of target genes remains an important open question. Previous comparative studies of gene expression have largely measured the abundance of messenger RNA, which is affected by post-transcriptional regulatory processes, hence limiting inferences about the mechanisms underlying expression differences. Here, we directly measured nascent transcription in primate species, allowing us to separate transcription from post-transcriptional regulation. We used precision run-on and sequencing to map RNA polymerases in resting and activated CD4+ T cells in multiple human, chimpanzee and rhesus macaque individuals, with rodents as outgroups. We observed general conservation in coding and non-coding transcription, punctuated by numerous differences between species, particularly at distal enhancers and non-coding RNAs. Genes regulated by larger numbers of enhancers are more frequently transcribed at evolutionarily stable levels, despite reduced conservation at individual enhancers. Adaptive nucleotide substitutions are associated with lineage-specific transcription and at one locus, SGPP2, we predict and experimentally validate that multiple substitutions contribute to human-specific transcription. Collectively, our findings suggest a pervasive role for evolutionary compensation across ensembles of enhancers that jointly regulate target genes.