It means to be fast. e.g. I hope that this class will be on their running clocks and hand in their essays on time.

Yeah, I haven't heard of "be on running clocks" too. The closest one I can find in my dictionary is "run out the clock" or "kill the clock". "Run out the clock" means to use up as much game time as possible when one is winning, as to protect a lead in basketball, ice hockey, or football. For example: The Pistons thought they were running out the clock but lost the ball and the game in the last nine seconds.

Hello Linky, There is ' to run out the clock' and it has a specific meaning specially in football matches ,it means to keep the ball away from the team competing against you at the end of a game so that they cannot score any point.

Hi Linky. I've not heard that phrase either. Can you give an example of where you have seen or heard it?

to tell you the truth I have personally never ever heard this phrase before in my life. But I guess it kind of sounds like you can use it when you have a tight schedule, and you have a time limit to get everything done.