If the old and new filesystems are both accessible to your machine, then consider using a symbolic link instead of rsync. If your rsync command you're using does not specify hosts (or if they are the same host), then this is the case. You're trying to mirror two directories with a different name on the same host. Don't use rsync for this, since you are duplicating the data, and you will have to run your rsync often to keep them in sync.
Using a symbolic link is a one-time fix that will mirror two directories (with different names) and requires almost no space. It's like creating an alias directory that points to another directory.
Let's say you had the old git in a directory called /old/path/old_git and now the code repository has moved to /new/path/new_git
You can do:
rm -rf old_git (if you still have it there, get rid of it, or move it out of the way)
ln -s /new/path/new_git old_git
This will create a link as such:
/old/path/old_git -> /new/path/new_git
So that anything that is put into new_git will be instantly available the old way as well, without duplicating data, and without having to constantly sync them.