In cells lacking telomerase, telomeres gradually shorten during each cell division to reach a critically short length, permanently activate the DNA damage checkpoint, and trigger replicative senescence. The increase in genome instability that occurs as a consequence may contribute to the early steps of tumorigenesis. However, because of the low frequency of mutations and the heterogeneity of telomere-induced senescence, the timing and mechanisms of genome instability increase remain elusive. Here, to capture early mutation events during replicative senescence, we used a combined microfluidic-based approach and live-cell imaging in yeast. We analyzed DNA damage checkpoint activation in consecutive cell divisions of individual cell lineages in telomerase-negative yeast cells and observed that prolonged checkpoint arrests occurred frequently in telomerase-negative lineages. Cells relied on the adaptation to the DNA damage pathway to bypass the prolonged checkpoint arrests, allowing further cell divisions despite the presence of unrepaired DNA damage. We demonstrate that the adaptation pathway is a major contributor to the genome instability induced during replicative senescence. Therefore, adaptation plays a critical role in shaping the dynamics of genome instability during replicative senescence.