Post starburst E+A galaxies are thought to have experienced a significant starburst that was quenched abruptly. Their disturbed, bulge-dominated morphologies suggest that they are merger remnants. We present ESI/Keck observations of SDSS J132401.63+454620.6, a post starburst galaxy at redshift z = 0.125, with a starburst that started 400 Myr ago, and other properties, like star formation rate (SFR) consistent with what is measured in ultra luminous infrared galaxies (ULRIGs). The galaxy shows both zero velocity narrow lines, and blueshifted broader Balmer and forbidden emission lines (FWHM=1350 +- 240 km/s). The narrow component is consistent with LINER-like emission, and the broader component with Seyfert-like emission, both photoionized by an active galactic nucleus (AGN) whose properties we measure and model. The velocity dispersion of the broad component exceeds the escape velocity, and we estimate the mass outflow rate to be in the range 4-120 Mo/yr. This is the first reported case of AGN-driven outflows, traced by ionized gas, in post starburst E+A galaxies. We show, by ways of a simple model, that the observed AGN-driven winds can consistently evolve a ULIRG into the observed galaxy. Our findings reinforce the evolutionary scenario where the more massive ULIRGs are quenched by negative AGN feedback, evolve first to post starburst galaxies, and later become typical red and dead ellipticals.