We establish a general formulation for spin current pumped by magnons at the interface between a normal metal and a magnetic insulator, valid for any noncollinear magnetic configuration in the linear spin wave regime. This current is generated by driving the system in a nonequilibrium state, covering setups such as thermal spin injection (spin Seebeck effect) or spin voltage by irradiation of the insulator (spin pumping). We illustrate the formula in the special case of a honeycomb topological ferromagnet, for simplicity, and cover both the spin Seebeck and spin pumping setups. We show how the topological parameters influence the spin current and propose a way to obtain a contribution mainly from the topological edge magnons in the spin pumping case.