We describe Qonductor, a cloud orchestrator for hybrid quantum-classical applications that run on heterogeneous hybrid resources. Qonductor exposes the , a high-level and hardware-agnostic API for customizable hybrid application development and execution, that abstracts away the complexity of hybrid resource management. To guide hybrid resource management, the accurately estimates execution fidelity and runtime to generate and offer resource plans. The leverages the resource plans to automate job scheduling on hybrid resources and balance the tradeoff between users' objectives of high fidelity and low runtimes and the cloud operator's objective of resource efficiency. We implement an open-source prototype of Qonductor by building on top of Kubernetes and evaluate it using more than 7000 real quantum runs on the IBM quantum cloud to simulate real cloud workloads. Qonductor achieves up to 54\% lower job completion times (JCTs) while sacrificing 6\% fidelity, balances the load across QPU which increases quantum resource utilization by up to 66\%, and scales with increasing system sizes and loads.