We have grown nearly freestanding single-layer $1{T}^{\ensuremath{'}}\ensuremath{-}\mathrm{WT}{\mathrm{e}}_{2}$ on graphitized $6H$-SiC(0001) by using molecular beam epitaxy (MBE), and characterized its electronic structure with scanning tunneling microscopy/spectroscopy (STM/STS). The existence of topological edge states at the periphery of single-layer $\mathrm{WT}{\mathrm{e}}_{2}$ islands was confirmed. Surprisingly, a bulk band gap at the Fermi level and insulating behaviors were also found in single-layer $\mathrm{WT}{\mathrm{e}}_{2}$ at low temperature, which are likely associated with an incommensurate charge order transition. The realization of two-dimensional topological insulators (2D TIs) in single-layer transition-metal dichalcogenide provides a promising platform for further exploration of the 2D TIs' physics and related applications.