I have a folder application/, which I add to the .gitignore.
Inside the application/-folder there is a folder application/language/gr.

How can I include this folder?

I've tried this:

application/
!application/language/gr/

If you exclude application/, then everything under it will always be excluded (even if some later negative exclusion pattern (“unignore”) might match something under application/).

To do what you want, you have to “unignore” every parent directory of anything that you want to “unignore”. Usually you end up writing rules for this situation in pairs: ignore everything in a directory, but not some certain subdirectory.

# you can skip this first one if it is not already excluded by prior patterns
!application/
application/*
!application/language/
application/language/*
!application/language/gr/

Note
The trailing /* is significant:

• The pattern dir/ excludes a directory named dir and (implicitly) everything under it.
  With dir/, Git will never look at anything under dir, and thus will never apply any of the “un-exclude” patterns to anything under dir.
• The pattern dir/* says nothing about dir itself; it just excludes everything under dir. With dir/*, Git will process the direct contents of dir, giving other patterns a chance to “un-exclude” some bit of the content (!dir/sub/).