  In this article, we introduce the notion of star-Ricci tensors in the real
hypersurfaces of complex quadric $Q^m$. It is proved that there exist no Hopf
hypersurfaces in $Q^m,m\geq3$, with commuting star-Ricci tensor or parallel
star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci
solitons on $M$ are considered. In this case we show that $M$ is an open part
of a tube around a totally geodesic $\mathbb{C}P^\frac{m}{2}\subset
Q^{m},m\geq4$.
