  Magnetic susceptibility, specific heat, and muon spin relaxation ($\mu$SR)
measurements have been performed on a newly synthesized three-dimensional
sandglass-type lattice Tm$_3$SbO$_7$, where two inequivalent sets of
non-Kramers Tm$^{3+}$ ions (Tm$^{3+}_1$ and Tm$^{3+}_2)$ show crystal
electrical field effect at different temperature ranges. The existence of an
ordered or a glassy state down to 0.1~K in zero field is excluded. The
low-energy properties of Tm$_3$SbO$_7$ are dominated by the lowest non-Kramers
quasi-doublet of $\rm Tm^{3+}_1$, and the energy splitting is regarded as an
intrinsic transverse field. Therefore, the low-temperature paramagnetic
phenomenon in Tm$_3$SbO$_7$ is explained by a transverse field Ising model,
which is supported by the quantitative simulation of specific heat data. In
addition, the perturbation from Tm$^{3+}_2$ may play an important role in
accounting for the low temperature spin dynamics behavior observed by $\mu$SR.
