Light-induced ferroelectricity in quantum paraelectrics is a new avenue of achieving dynamic stabilization of hidden orders in quantum materials. In this Letter, we explore the possibility of driving a transient ferroelectric phase in the quantum paraelectric KTaO_{3} via intense terahertz excitation of the soft mode. We observe a long-lived relaxation in the terahertz-driven second harmonic generation (SHG) signal that lasts up to 20 ps at 10 K, which may be attributed to light-induced ferroelectricity. Through analyzing the terahertz-induced coherent soft-mode oscillation and finding its hardening with fluence well described by a single-well potential, we demonstrate that intense terahertz pulses up to 500  kV/cm cannot drive a global ferroelectric phase in KTaO_{3}. Instead, we find the unusual long-lived relaxation of the SHG signal comes from a terahertz-driven moderate dipolar correlation between the defect-induced local polar structures. We discuss the impact of our findings on current investigations of the terahertz-induced ferroelectric phase in quantum paraelectrics.