I think they'll have to recast. They can't kill off the character of Chekov just because this guy died unexpectedly.
-PJ
I don’t know if they will recast or not. If this had happened after the first movie, I have no doubt they would recast. But after three movies, it will be a hard call.
Since Abrams established this particular series of movies as an alternate timeline, they might kill off Chekov and bring in a new character.