  Let $\mathcal{OG}(4)$ denote the family of all graph-group pairs $(\Gamma,
G)$ where $\Gamma$ is finite, 4-valent, connected, and $G$-oriented
($G$-half-arc-transitive). A subfamily of $\mathcal{OG}(4)$ has recently been
identified as `basic' in the sense that all graphs in this family are normal
covers of at least one basic member. In this paper we provide a description of
such basic pairs which have at least one $G$-normal quotient which is
isomorphic to a cycle graph. In doing so, we produce many new infinite families
of examples and solve several problems posed in the recent literature on this
topic. This result completes a research project aiming to provide a description
of all basic pairs in $\mathcal{OG}(4)$.
