This paper presents the problem of controlling multiple tasks in a prioritized scheme during accidental external physical interaction with redundant robot. This issue arises when robots are employed in social, unknown, dynamic environments for complex and critical missions. Exploiting robot redundancy to ensure safety and compliance during performing hierarchical tasks is considered in this work. A general approach to control the main task (position/orientation of the end-effector) with allocated priorities beside compliance behavior in the null space of the tasks is proposed. External interactions on the robot body are estimated with an appropriate observer without using any force/torque sensors which is further used to bring compliance in the redundant space. A novel task allocation method is proposed and the convergence of the task space error, interaction estimation error as well as null space velocities are guaranteed. Finally, the performance of the method is investigated through computer simulation and real experiments on KUKA robot arm.