We investigate a distributed-satellite-clusters (DSC)-system-based spectrum sensing, to enhance the ability for sensing weak signals. However, the spectrum-sensing performance may be significantly decreased by the phase deviations among different satellite clusters, where the deviations may be caused by the movement and the perturbation of satellites. To eliminate such a decrement, we propose a cooperative spectrum-sensing scheme in the presence of phase deviations, where the deviations are alleviated by a special two-stage phase synchronization. Specifically, the phase compensation is first performed relying on broadcasting reference signals and the ephemeris, to address the challenges of the deviations caused by the movement. Then, a two-bit feedback algorithm, having a dynamic disturbance step size, is further adopted for controlling and mitigating the deviations caused by the perturbation. Additionally, we provide the closed-form expression of the correct detection probability of the proposed spectrum-sensing scheme, using the specially derived probability density function of the sum of the shadowed-Rician random variables with independently identical distribution. Simulation results show that the proposed scheme can achieve the best spectrum-sensing performance, comparing with the traditional energy detection, eigenvalue ratio test and the generalized likelihood ratio test.