Is it possible to push the changes in the .git directory to a remote repository?
I wish to have a common project description and not have to re-enter it for all the clones of my repository.
It's strange that the project description is something that is not common to each clone.
Answer
You could store a description (or .description, if you don't want it to be visible) in the root of your repo, and then symlink .git/description to that in each repo, like so:
repo/
.description
.git/
description -> ../.description
You'd have to set up the symlink manually in each of your repos, but you'd only have to do that once (when the repo is created).
Or you could use a post-receive hook to copy your tracked description file into .git/description. You'd have to set up that hook on each remote repo, too, but again, that would only need to happen once (when the repo is created).