We present acoustic signatures of the electric quadrupolar degrees of freedom in the honeycomb-layer compound UNi_{4}B. The transverse ultrasonic mode C_{66} shows softening below 30 K both in the paramagnetic phase and antiferromagnetic phases down to ∼0.33 K. Furthermore, we traced magnetic field-temperature phase diagrams up to 30 T and observed a highly anisotropic elastic response within the honeycomb layer. These observations strongly suggest that Γ_{6}(E_{2g}) electric quadrupolar degrees of freedom in localized 5f^{2} (J=4) states are playing an important role in the magnetic toroidal dipole order and magnetic-field-induced phases of UNi_{4}B, and evidence some of the U ions remain in the paramagnetic state even if the system undergoes magnetic toroidal ordering.