An accurate potential energy surface (PES) for the lowest lying A′′4 state of the CNO system is presented based on explicitly correlated multi-reference configuration interaction calculations with quadruple zeta basis set (MRCI-F12/cc-pVQZ-F12). The ab initio energies are fitted using the double many-body expansion method, thus incorporating long-range energy terms that can accurately describe the electrostatic and dispersion interactions with physically motivated decaying functions. Together with the previously fitted lowest A′2 and A′′2 states using the same theoretical framework, this constitutes a new set of PESs that are suitable to predict rate coefficients for all atom–diatom reactions of the CNO system. We use this set of PESs to calculate thermal rate coefficients for the C(P3) + NO(Π2) reaction and compare the temperature dependence and product branching ratios with experimental results. The comparison between theory and experiment is shown to be improved over previous theoretical studies. We highlight the importance of the long-range interactions for low-temperature rate coefficients.