CRISPR-Cas pathways provide prokaryotes with acquired "immunity" against foreign genetic elements, including phages and plasmids. Although many of the proteins associated with CRISPR-Cas mechanisms are characterized, some requisite enzymes remain elusive. Genetic studies have implicated host DNA polymerases in some CRISPR-Cas systems but CRISPR-specific replicases have not yet been discovered. We have identified and characterised a family of CRISPR-Associated Primase-Polymerases (CAPPs) in a range of prokaryotes that are operonically associated with Cas1 and Cas2. CAPPs belong to the Primase-Polymerase (Prim-Pol) superfamily of replicases that operate in various DNA repair and replication pathways that maintain genome stability. Here, we characterise the DNA synthesis activities of bacterial CAPP homologues from Type IIIA and IIIB CRISPR-Cas systems and establish that they possess a range of replicase activities including DNA priming, polymerisation and strand-displacement. We demonstrate that CAPPs operonically-associated partners, Cas1 and Cas2, form a complex that possesses spacer integration activity. We show that CAPPs physically associate with the Cas proteins to form bespoke CRISPR-Cas complexes. Finally, we propose how CAPPs activities, in conjunction with their partners, may function to undertake key roles in CRISPR-Cas adaptation.