We have investigated the dielectric properties of a 17.2 mol % mixture of chlorobenzene and decalin in the supercooled and in the glassy state under hydrostatic pressure up to 400 MPa. The dielectric loss shows the well-known primary (alpha) relaxation and a secondary (beta) relaxation the origin of which is still being debated. The glass transition temperature T-g increases linearly with pressure. The fragility is pressure independent. With increasing pressure the relaxation strength of the beta process rises at the expense of the alpha process. Above around 160 K, where devitrification occurs at atmospheric pressure, the activation energy of the secondary relaxation process is roughly twice that at lower temperatures. Both energies are proportional to T-g, indicating a strong correlation between alpha and beta processes. A possible origin of the secondary relaxation is rationalized by critical clusters in the melt.