Superconductivity has been observed in many insulating transition metal dichalcogenides (TMDCs) under pressure. However, the origin of superconductivity remains elusive due to the lack of studies on their structures at low temperatures. Here, we report the observation of a high-T_{c} superconducting state (SC-I phase) coexisting with other superconducting states in a compressed 1T-HfS_{2} crystal up to approximately 160 GPa. In situ synchrotron x-ray diffraction results exclude the presence of decomposed sulfur and confirm two structural phase transitions at room temperature, as well as an additional transition at low temperature, which contribute to the emergence of multiple superconducting states. The SC-I phase exhibits an unsaturated T_{c} of 16.4 K at 158 GPa, and demonstrates the highest upper critical field among the bulk TMDCs, μ_{0}H_{c2}(0)≈29.7 T for a T_{c}∼15.2 K at 147 GPa, exceeding the weak-coupling Pauli limit. These results reveal abundant SC properties together with sensitive structures in compressed HfS_{2}, and thereby extend our understanding on TMDCs' superconductivity.