What will happen to the narrator after the story in "The Pit and the Pendulum"?

There is no real "correct" answer to this question, unfortunately, but there are some things that can be speculated upon. For instance, at the end of the story, the narrator is saved from his death in the pit by the Frenchman General Lasalle. The narrator tells us that General Lasalle was a part of the French army, and that army had taken over his prison, the city of Toledo, and apparently the Inquisition (of course, by saying “The Inquisition was in the hands of its enemies”, the narrator could just mean the branch of the Inquisition in that particular city, or he could mean the Inquisition in its entirety—either way, it is not historically accurate). But considering he was saved from his death initially, it is more than likely that he is saved from death permanently, so the narrator was probably questioned about his time in the prison and then allowed to return home.

Of course, as I said, nothing is certain—this is all merely speculation.