This study focuses on stabilizing Reduced Order Model based on Proper Orthogonal Decomposition (POD) and on improving the POD functional subspace. A modified reduced order model (ROM) that incorporates directly the pressure term is proposed. The ROM is obtained by seeking a solution that lives in the POD subspace and at the same time minimizes the Navier-Stokes residuals. Both ROM stabilization and POD subspace adaptation make use of methods based on the fine scale equation that is approximated using the residuals of the Navier-Sokes equations. Results are shown for the 2D confined cylinder wake flow.