  Novel materials incorporating electronic degrees of freedom other than
charge, including spin, orbital or valley \textit{et al} have manifested
themselves to be of the great interests and applicable potentials. Recently,
the multipolar degrees of freedom have attracted remarkable attention in the
electronic correlated effects. In this work, we systematically studied the
transport, magnetic and thermodynamic properties of the topological semimetal
candidate PrBi in the framework of crystalline electric field theory. Our
results demonstrate the $\Gamma_3$ non-Kramers doublet as the ground state of
Pr$^{3+}$ (4$f^2$) ions. This ground state is nonmagnetic but carries a
non-zero quadrupolar moment $\langle\hat{O}_2^0\rangle$. A quadrupolar phase
transition is inferred below 0.08 K. No obvious quadrupolar Kondo effect can be
identified. Ultrahigh-field quantum oscillation measurements confirm PrBi as a
semimetal with non-trivial Berry phase and low total carrier density 0.06 /f.u.
We discuss the interplay between low carrier density and $4f^2$ quadrupolar
moment, and ascribe the weak quadrupolar ordering and Kondo effect to
consequences of the low carrier density. PrBi, thus, opens a new window to the
physics of topology and strongly correlated effect with quadrupolar degrees of
freedom in the low-carrier-density limit, evoking the need for a reexamination
of the Nozi\`{e}res exhaustion problem in the context of multi-channel Kondo
effect.
