They will probably get a new Chekov and act like nothing has changed.
There have been other cases where new actors take the place of old ones. John-Boy Walton comes to mind. They had a new John-Boy for a while. They had a new replacement Becky on Roseanne Barr’s show. It happens. Chekov was a major character so I expect they will replace him, not have him get killed off.
In Jimmy “JJ Dynomite!” Walker’s stand up routine he mentioned that he auditioned for the Waltons to play the part of Boy-Boy.