During replication, a sliding clamp, which is a β-subunit in bacteria or proliferating cell nuclear antigen - PCNA - in eukaryotes, fastens the polymerase to the DNA as it moves along the strand, catalyzing the new DNA synthesis. 

When this replicative polymerase gets stalled on a damaged base or region, specialized enzymes covalently modify this sliding clamp through the addition of ubiquitin or SUMO proteins. The modification triggers the release of the replicative polymerase and recruitment of a special polymerase called Translesion DNA polymerase, or TLS polymerase, to the damaged site through interactions with the clamp. 

Next, the TLS polymerase inserts a nucleotide across the damaged site in a process called “Translesion DNA synthesis”. Once the nascent DNA chain has extended beyond the lesion, the chemical modification is detached from the clamp, and the TLS polymerase is switched with the cell’s replicative DNA polymerase.  With the binding of the replicative polymerase, accurate DNA replication resumes.

Unlike damage repair, there is no restoration to the original DNA sequence, and the damage or lesion will still be present in the DNA, so the phenomenon is described as damage tolerance. 

During replication, while some TLS polymerases can add the correct nucleotides to the new strand by chance, others may be prone to errors that give rise to mutations. The type of lesion often determines the accuracy of the polymerase. For example - where the error is an abasic site, there is no coding information for the polymerase to add the correct nucleotide during replication. In archaea, the polymerase Dpo4 preferentially adds an Adenine opposite an abasic site - but other polymerases may fix similar lesions in different ways.