There's no set time. When the devs are looking for more they'll make a forum thread with the application.
Make me a mod, I've reported quite a lot and I've stripped my stats so it makes me a perfect candidate. 😐
You should know that asking to be made a mod is not what gets you the spot. Stats are also irrelevant. You can read the application FAQ for information and I suggest checking out the silencing and bans guide, as well as the newest policy updates.
In a few more years probably, or I guess whenever they need new ones. They usually post it here on forums. You'll also be able to see it on Campus Buzz.
I recommend familiarizing yourself with the FAQ and the ToU. Also the most recent rule updates. This guide has more also if you're interested.