The sequential contact transformation technique is applied to the nuclear quadrupole coupling operator for a molecule containing a threefold symmetric internal rotor in order to be consistent with the transformed vibration-torsion-rotation Hamiltonian to be used in the analysis of the spectra of the molecule. Various higher-order effects on the nuclear quadrupole coupling energies, such as the centrifugal distortion, the anharmonic corrections and so on, are formulated for a molecule containing one quadrupolar nucleus. The detailed discussion is presented of vibrational-torsional-rotational dependence of these higher corrections to the quadrupole hyperfine energies.