  Future experiments dedicated to the detection of Coherent Elastic
Neutrino-Nucleus Scattering may be powerful tools in probing light new physics.
In this paper we study the sensitivity on light $Z'$ mediators of two proposed
experiments: a directional low pressure Time Projection Chamber detector,
$\nu$BDX-DRIFT, that will utilize neutrinos produced at the Long Baseline
Neutrino Facility, and several possible experiments to be installed at the
European Spallation Source. We compare the results obtained with existing
limits from fixed-target, accelerator, solar neutrino and reactor experiments.
Furthermore, we show that these experiments have the potential to test
unexplored regions that, in some case, could explain the anomalous magnetic
moment of the muon or peculiar spectral features in the cosmic neutrino
spectrum observed by IceCube.
