We present a joint experimental and computational study of second harmonic generation and Kerr effect induced by intense terahertz electric fields in the quantum paraelectric material KTaO 3 .The single-cycle THz electric pulses induce the free induction decay of the polar soft phonon mode and a ferroelectric polarization response that lasts for several picoseconds in both experiment and computation. We observe a much longer-lasting (43 ps) transient Kerr effect that follows the THz excitation. We explain the disparity in the relaxation times between the THz-induced second harmonic generation and Kerr effect by the presence of the polar nanoregions intrinsic to KTaO 3 .The origin of the slow THz Kerr effect dynamics is not presently understood. We speculate that it may be associated with the rotational motion of polar nanoregions due to the materials proximity to the ferroelectric phase transition.