Trimaximal mixing pattern (TM1) of the neutrino mixing matrix is consistent with current neutrino oscillation data. In this work, we have investigated the phenomenology of inverse neutrino mass matrix ((m_{nu }^{{ - 1}})) with one-zero textures considering neutrino mixing matrix to be of TM1 type. There are six possible patterns of (m_{nu }^{{ - 1}}) with one-zero. We have obtained the predictions for the least known neutrino sector parameters such as octant of atmospheric mixing angle, ({{theta }_{{23}}}), Dirac-type CP violating phase, δ, and effective Majorana neutrino mass, ({{m}_{{ee}}}). One of the generic feature of this class of model is the existence of necessary CP violation, i.e., Dirac CP phase δ is non-zero. For maximal value of ({{theta }_{{23}}} = 45^circ ), the model predicts maximal CP violation. The (0nu beta beta ) decay experiments have imperative consequences for viability of one-zero texture in (m_{nu }^{{ - 1}}). It will either refute a model completely or have distinguishing implications for neutrino mass ordering in a model. We have also proposed two possible scenarios in which such phenomenological conjecture may be realized using non-Abelian discrete flavor symmetry group ({{A}_{4}}) and cyclic group ({{Z}_{3}}).