Photoelectron spectroscopy experiments in ionic solutions reveal important electronic structure information, in which the interaction between hydrated ions and water solvent can be inferred. Based on many-body perturbation theory with GW approximation, we theoretically compute the quasiparticle electronic structure of chloride anion solution, which is modeled by path-integral $ab$ $initio$ molecular dynamics simulation by taking account the nuclear quantum effects (NQEs). The electronic levels of hydrated anion as well as water are determined and compared to the recent experimental photoelectron spectra. It is found that NQEs improve the agreement between theoretical prediction and experiment because NQEs effectively weaken the hybridization of the between the $rm Cl^-$ anion and water. Our study indicates that NQEs plays a small but non-negligible role in predicting the electronic structure of the aqueous solvation of ions of the Hofmeister series.
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