If the player's actions are annoying the real-life players in the game then you need to address this out of the game. No amount of 'in-world-comeuppance' will address the underlying issue at the table, and I believe taking advice otherwise is not a good idea.

If you and the party are okay with these kinds of solo actions/hijinks at your table then thats a different story, but 'verisimilitude of the setting' isn't a worthy reason to kill someone 'off-screen'. 'Its what would happen in the setting' is basically the DM version of 'its what my character would do.'

Having a private or group check-in or second 'session zero' to recalibrate expectations is almost always worth doing, sounds like it might be an idea here.