DNA polymerase specifically involved in the DNA repair by translesion synthesis (TLS). Plays an important role in translesion synthesis, where the normal high-fidelity DNA polymerases cannot proceed and DNA synthesis stalls. Inserts one or 2 nucleotide(s) opposite the lesion. During homologous recombination (HR) repair, has a overlapping role with the error-prone translesion polymerase PolZ1/DNApol-zeta to initiate repair synthesis that is completed by end joining or another polymerase that can bind and reinitiate synthesis. Particularly important for the repair of UV-induced pyrimidine dimers and for hydroxyurea (HU)-induced DNA damage. Although inserts the correct base, may cause base transitions and transversions depending upon the context. Forms a Schiff base with 5'-deoxyribose phosphate at abasic sites, but does not have any lyase activity, preventing the release of the 5'-deoxyribose phosphate (5'-dRP) residue. This covalent trapping of the enzyme by the 5'-dRP residue inhibits its DNA synthetic activity during base excision repair, thereby avoiding high incidence of mutagenesis 