Hunter x Hunter went into hiatus on chapter 400 back in December 2022. If it resumes publication in the near future, when will chapter 401 be releasesd?

Resolves based on the Japanese release date. If it's released on a serialized magazine (like Shonen Jump) then it resolves to the day that magazine is released (mondays for Shonen Jump for example). If it releases digitally, then resolves to the day it is first available in Japan. If it releases in both formats, only the one that comes out first resolves this question.

Resolves "Never" if the series is officially cancelled (on any publication).

This market generally assumes it will come out sometime in 2024 based on Togashi's recent tweets, as well as this market's probabilty: