How will Gon continue fighting after his fight with Neferpitou? During the Chimera Ants Arc, after Gon fights with Neferpitou,


   Gon lost his Nen.


Will he be able to fight and continue advancing within the Hunter x Hunter Universe?
Without nen, Gon won't be able to fight against Nen users. As was seen in the Heaven's Arena arc, the only way to defend against Nen is with Nen, and without it even relatively weak attacks will kill or cripple you.

At the moment, the story is on an indefinite hiatus, but if it ever gets going properly again, Gon will not be able to fight against Nen users unless somehow he is able to regain his Nen, whether by himself or by someone helping him. 

It's obviously a different story, but I think it's similar to how after Ichigo lost his spiritual pressure in Bleach, he was pretty weak for a while until it was restored to him.

Alluka was able to save Gon, and it's definitely possible that either some Hunter has the capability to restore Gon's Nen, or that somewhere in the Dark Continent there will be a way of restoring it.