The pressure evolution of the Raman active electronic excitations of the transition metal dichalcogenides 2H-TaS_{2} is followed through the pressure phase diagram embedding incommensurate charge-density-wave and superconducting states. At high pressure, the charge-density wave is found to collapse at 8.5 GPa. In the coexisting charge-density-wave and superconducting orders, we unravel a strong in-gap superconducting mode, attributed to a Higgs mode, coexisting with the expected incoherent Cooper-pair breaking signature. The latter remains in the pure superconducting state reached above 8.5 GPa. Our report constitutes a new observation of such Raman active Higgs mode since the long-standing unique case 2H-NbSe_{2}.