We discuss the stabilisation problem of a constrained one-link flexible arm with boundary disturbance flowing to the control end. By the active disturbance rejection control (ADRC) approach, we first design a time varying high gain extended state observer to estimate the disturbance, and then give a feedback controller to eliminate the negative effect of the disturbance. The well-posedness of the closed-loop system is proved by the semigroup theory. Moreover, under different assumptions of the time varying high gain function, we obtain the asymptotical stability and the exponential stability of the closed-loop system, respectively. Finally, some numerical simulations are presented to support the theoretical results.