The replisome must overcome DNA damage to ensure complete chromosome replication. Here, we describe the earliest events in this process by reconstituting collisions between a eukaryotic replisome, assembled with purified proteins, and DNA damage. Lagging-strand lesions are bypassed without delay, leaving daughter-strand gaps roughly the size of an Okazaki fragment. In contrast, leading-strand polymerase stalling significantly impacts replication fork progression. We reveal that the core replisome itself can bypass leading-strand damage by re-priming synthesis beyond it. Surprisingly, this restart activity is rare, mainly due to inefficient leading-strand re-priming, rather than single-stranded DNA exposure or primer extension. We find several unanticipated mechanistic distinctions between leading- and lagging-strand priming that we propose control the replisome’s initial response to DNA damage. Notably, leading-strand restart was specifically stimulated by RPA depletion, which can occur under conditions of replication stress. Our results have implications for pathway choice at stalled forks and priming at DNA replication origins. Display omitted •Reconstitution of collisions between a eukaryotic replisome and DNA damage•Leading-strand damage specifically causes fork stalling and uncoupling•The eukaryotic replisome can re-initiate leading-strands downstream of DNA damage•Multiple mechanistic differences exist between leading- and lagging-strand priming To study the earliest events following DNA polymerase stalling during replication, Taylor and Yeeles reconstituted collisions between a yeast replisome assembled with purified proteins and template DNA damage. Surprisingly, re-priming of leading-strand synthesis beyond damage is inefficient but is promoted by RPA depletion, whereas lagging-strand priming occurs robustly after damage.