In this paper, we consider a partially clamped plate which is stiffened on a portion of its free boundary. Our aim is to build an asymptotic expansion of the displacement, solution of the Kirchhoff-Love model, with respect to the thickness of the stiffener. Due to the mixed boundary conditions, singularities appear, obstructing the construction of the terms of the asymptotic expansion in the same way as if the plate was surrounded by the stiffener on its whole boundary. Using a splitting into regular and singular parts, we are able to formulate an asymptotic expansion involving profiles which allow to take into account the singularities.