The maintenance of genome stability requires efficient leading strand synthesis by DNA Polymerase Epsilon (Pol). By performing CRISPR genetic screens in cells lacking the POLE4 subunit of Pol we define a genetic map of the factors required to support Pol function in the absence of its accessory subunits. A set of genes involved in iron metabolism emerge as required to sustain Iron Sulphur Cluster (ISC)-dependent Pol activity. We then dissect a synthetic lethal interaction between POLE3-POLE4 and the CHTF18-RFC2/5 complex. By combining cell biology, structural modelling and biochemistry, we define the existence of two tiers of regulation of Pol processivity: leading strand-specific loading of PCNA by CHTF18-RFC2/5 and “gripping” of newly synthesised dsDNA by POLE3-POLE4. The combined loss of these functions is incompatible with leading strand synthesis and viability. In summary, we describe the biochemical basis of human leading strand synthesis and the consequence of its dysfunction in genome stability.