In this paper, we develop a framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the semiclassical limit of quantum integrable systems. We start with an outline of the concept of hybrid dynamical systems. Then, we give several examples of hybrid integrable systems. The first series of examples is a class of hybrid integrable systems that appear in the semiclassical limit of quantum spin chains. Then, we look at the semiclassical limit of the quantum spin Calogero–Moser–Sutherland (CMS) system. The result is a hybrid integrable system driven by usual classical Calogero–Moser–Sutherland dynamics. This system at the fixed point of the multi-time classical dynamics CMS system gives the commuting spin Hamiltonians of Haldane–Shastry model. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.