NaCr2O4 is a Q1D TMO that offers a rich range of properties from the view point of fundamental science as well as from the view point of applied science. Indeed on one hand NaCr2O4 shows unconventional colossal magnetoresistance, spin frustration of the zigzag chains, mixed valence, on the other hand it could also be a good candidate as a cathode material in batteries, because of its crystal structure with the Na-ion aligned along the 1D CrO6 channels (very similar to the famous battery cathode material LiFePO4). Indeed, parallel investigations of ion diffusion in this sample are already planned. To the best of our knowledge, a systematic pressure dependent neutron study of NaCr2O4 has never been performed, therefore our unexpected result obtained in a previous experiment (suppression of magnetic transition temperature) encouraged us to propose further investigations in this direction.