We consider the wave equation with mixed boundary conditions in a bounded domain; on one portion of the boundary, we have dynamic Wentzell boundary conditions, and on the other portion, we have homogeneous Dirichlet boundary conditions. First, using an appropriate geometric partition of the boundary, we prove some Carleman estimates for this system. Then, we apply those estimates to prove a boundary controllability result for a nonconservative model of the system under consideration. Our results improve earlier Carleman estimates and boundary controllability results established in the Dirichlet boundary conditions setting.