[JRutledge]

All officials are in charge of the time clock at all times of the game.

If you are asking who has the last second shot, then that is the opposite table official who is either the Center or Trail if you are using the common mechanics. Your state, area or association might have another way to do this. As I said before, all officials need to take responsibility for the clock because only the one with the last second shot might not be aware that clock did not start properly and you need to take action.

Peace