Anti-Clustered regularly interspaced small palindromic repeat (CRISPR) (Acr) phages cooperate to establish a successful infection in CRISPR-containing host. We report here the selective advantage provided by a replication initiator, Rep, toward cooperative host immunosuppression by viruses encoding Acrs. A rep knockout mutant (Δgp16) of Sulfolobus islandicus rod-shaped virus 2 produced around fourfold less virus in a CRISPR-null host, suggesting that Rep is the major replication initiator. In addition to Rep-dependent replication initiation from the viral genomic termini, we detected Rep-independent replication initiation from nonterminal sites. Intriguingly, despite the presence of Acrs, lack of Rep showed a profound effect on virus propagation in a host carrying CRISPR-Cas immunity. Accordingly, the co-infecting parental virus (rep-containing) outcompeted the Δgp16 mutant much more quickly in the CRISPR-containing host than in CRISPR-null host. Despite the nonessentiality, rep is carried by all known members of Rudiviridae, which is likely an evolutionary outcome driven by the ubiquitous presence of CRISPR-Cas in Sulfolobales.