Cloud computing is a distributed computing model which renders services for cloud users around the world. These services need to be rendered to customers with high availability and fault tolerance, but there are still chances of having single-point failures in the cloud paradigm, and one challenge to cloud providers is effectively scheduling tasks to avoid failures and acquire the trust of their cloud services by users. This research proposes a fault-tolerant trust-based task scheduling algorithm in which we carefully schedule tasks within precise virtual machines by calculating priorities for tasks and VMs. Harris hawks optimization was used as a methodology to design our scheduler. We used Cloudsim as a simulating tool for our entire experiment. For the entire simulation, we used synthetic fabricated data with different distributions and real-time supercomputer worklogs. Finally, we evaluated the proposed approach (FTTATS) with state-of-the-art approaches, i.e., ACO, PSO, and GA. From the simulation results, our proposed FTTATS greatly minimizes the makespan for ACO, PSO and GA algorithms by 24.3%, 33.31%, and 29.03%, respectively. The rate of failures for ACO, PSO, and GA were minimized by 65.31%, 65.4%, and 60.44%, respectively. Trust-based SLA parameters improved, i.e., availability improved for ACO, PSO, and GA by 33.38%, 35.71%, and 28.24%, respectively. The success rate improved for ACO, PSO, and GA by 52.69%, 39.41%, and 38.45%, respectively. Turnaround efficiency was minimized for ACO, PSO, and GA by 51.8%, 47.2%, and 33.6%, respectively.