Some kind of forumbot.
 

I am running a clan forum at the moment and I'd like to see if there is a plugin out that whenever someone makes a new thread in the "Recruitement Forum", there is made an automatic duplication of that thread but in another forum, a forum where only the "core" has access to. (and where we will discuss this person's application in private)

I've searched for something similar but couldn't find anything.

Hmm,

I started learning vB on a gaming site long long ago in a galaxy far far away...

Long story short for forms requesting information or an application to an army or side I always found this useful:

https://vborg.vbsupport.ru/showthread.php?t=234385

There is also info in the thread to help you make it post to another forum so one to the forum members can also view their application and one to the forum for staff to review, you can also code up your own custom output as Bananalive included that option ;). Very useful imo.

See if that can help with this and it should also be very useful on your site, you can create any type of form and use them in different ways to promote your community and interaction.