We report the effect of hydrostatic pressure on the magnetotransport properties of the Weyl semimetal NbAs. Subtle changes can be seen in the $rho_{xx}(T)$ profiles with pressure up to 2.31 GPa. The Fermi surfaces undergo an anisotropic evolution under pressure: the extremal areas slightly increase in the $mathbf{k_x}$-$mathbf{k_y}$ plane, but decrease in the $mathbf{k_z}$-$mathbf{k_y}$($mathbf{k_x}$) plane. The topological features of the two pockets observed at atmospheric pressure, however, remain unchanged at 2.31 GPa. No superconductivity can be seen down to 0.3 K for all the pressures measured. By fitting the temperature dependence of specific heat to the Debye model, we obtain a small Sommerfeld coefficient $gamma_0=$ 0.09(1) mJ/(mol$cdot$K$^2$) and a large Debye temperature, $Theta_D=$ 450(9) K, confirming a hard crystalline lattice that is stable under pressure. We also studied the Kadowaki-Woods ratio of this low-carrier-density massless system, $R_{KW}=$ 3.2$times 10^4$ $muOmega$ cm mol$^2$ K$^2$ J$^{-2}$. After accounting for the small carrier density in NbAs, this $R_{KW}$ indicates a suppressed transport scattering rate relative to other metals.