•Character of easy axis - electric field coupling affects the character of orientation instability of nematic cell.•Electro-sensitive easy axis noticeably changes the director field deformation in nematic cell in applied electric field.•Electro-optical response of nematic cell depends on character of easy axis - electric field coupling. The orientational instability of a director in a planar flexoelectric nematic liquid crystal cell in a constant electric field oriented perpendicular to the cell substrates is investigated. The easy axis on the surface of one of the polymer substrates can change its orientation, which is due to the impact of the initial surface orientation, liquid crystal, and electric field. The influence of the latter leads to the reorientation of the elastic parts of the polymer molecules of the substrate, which is a consequence of the interaction of intrinsic or induced dipole moments with the electric field. The corresponding contribution of such an interaction to the surface free energy of the nematic is considered to be linear or quadratic in terms of the electric field strength E. It is established that the orientational instability of the director has a threshold in the case of quadratic effect of the electric field and is thresholdless if the effect is linear. The temporal behavior of the director after the application of voltage with the subsequent transition of the system to a stationary state and its return to the initial homogeneous state after switching off the voltage is studied. The characteristic turn-on/off times of the system and the time of reaching the stationary state are calculated and their dependence on the system parameters is investigated. The transmittance of the nematic liquid crystal cell is calculated for a normally incident light.