HORMAD1 expression is usually restricted to germline cells, but it becomes mis-expressed in epithelial cells in ~60% of triple-negative breast cancers (TNBCs), where it is associated with elevated genomic instability (1). HORMAD1 expression in TNBC is bimodal with HORMAD1-positive TNBC representing a biologically distinct disease group. Identification of HORMAD1-driven genetic dependencies may uncover novel therapies for this disease group. To study HORMAD1-driven genetic dependencies, we generated a SUM159 cell line model with doxycycline-inducible HORMAD1 that replicated genomic instability phenotypes seen in HORMAD1-positive TNBC (1). Using small interfering RNA screens, we identified candidate genes whose depletion selectively inhibited the cellular growth of HORMAD1-expressing cells. We validated five genes (ATR, BRIP1, POLH, TDP1 and XRCC1), depletion of which led to reduced cellular growth or clonogenic survival in cells expressing HORMAD1. In addition to the translesion synthesis (TLS) polymerase POLH, we identified a HORMAD1-driven dependency upon additional TLS polymerases, namely POLK, REV1, REV3L and REV7. Our data confirms that out-of-context somatic expression of HORMAD1 can lead to genomic instability and reveals that HORMAD1 expression induces dependencies upon replication stress tolerance pathways, such as translesion synthesis. Our data also suggest that HORMAD1 expression could be a patient selection biomarker for agents targeting replication stress.