Reducing dimensionality can induce profound modifications to the physical properties of a system. In two-dimensional TaS2 and TaSe2, the charge-density wave phase accompanies a Mott transition, thus realizing the strongly correlated insulating state. However, this scenario deviates from TaTe2 due to p–d hybridization, resulting in a substantial contribution of Te 5p at the Fermi level. Here, we show that, differently from the Mott insulating phase of its sister compounds, bilayer TaTe2 hosts a power-law (V-shaped) gap at the Fermi level reminiscent of a Coulomb gap. It suggests the possible role of unscreened long-range Coulomb interactions emerging in lowered dimensions, potentially coupled with a disordered short-range charge-density wave. Our findings reveal the importance of long-range interactions sensitive to interlayer screening, providing another venue for the interplay of complex quantum phenomena in two-dimensional materials.