We investigate the effect of long range correlation in the environment for random pinning models. For a type of environment based on a renewal construction, we are able to describe the phase transition from the delocalized phase to the localized one, giving the critical exponent for the free-energy, and proving that at the critical point, the trajectories are fully delocalized. These results contrast both with what happens for the pure model or more studied case of i.i.d. disorder. where the critical behavior depends on Harris Criterion.