When exposed single-stranded DNA accumulates at stalled or collapsed replication forks, the replication stress response is triggered to prevent genome instability. Leishmania are parasitic eukaryotes where gene expression is universally polycistronic and whose plastic genomes facilitate rapid adaptations in response to stress, with evidence implicating intrinsic replication stress as a source. Little is known about the Leishmania replication stress response. In this study, we reveal the global dynamics of the replication stress response in L. major promastigotes by performing ChIP-seq on three key replication stress response proteins, γH2A, RPA1 and RAD9, in the absence and presence of replication stress. We show that common hotspots of replication stress correlate with DNA replication initiation and transcription termination in Leishmania. When DNA replication is stalled, replication stress response factors accumulate at early S-phase origins, with a signal pattern reminiscent of bidirectional replication fork progression. Under conditions of chronic replication stress, increased accumulation of replication stress response factors emerges at wider sites of transcription initiation, suggesting Leishmania may possess compensatory strategies to limit the effects of replication stress and ensure DNA replication can complete under these conditions. In contrast, chronic replication stress enhances RSR factor accumulation at transcription termination sites, highlighting these regions as key replication stress hotspots in Leishmania. Lastly, variations in RPA dynamics in ATR-deficient cells uncover crucial roles of this protein kinase in managing polycistronic transcription and DNA replication, particularly under replication stress, in Leishmania.