This paper presents a hybrid adaptive law for safety-critical adaptive control of constrained continuous-time systems under the effect of unknown disturbances. The proposed adaptive law features a hybrid update law that, using a hysteresis-type mechanism, appropriately resets the estimate of the disturbance. In contrast to continuous-time adaptation laws for safety-critical control, our hybrid adaptive law relaxes the assumption typically imposed on the unknown disturbances as well as the behavior usually imposed around the boundary of the safe region. We illustrate the benefits of the proposed hybrid law in an adaptive cruise control problem.