It is possible to set up Overleaf as a remote repository such that you can use it as an interface for a local repository. Then whenever you make a change on Overleaf, and compile, you can run git pull overleaf master to pull the changes from Overleaf to your local repo.
If you want to collaborate with others on a latex file and use Overleaf, using Overleaf as a remote repository can be problematic as it is difficult to manage conflicts.
Main References
- Section Creating an Overleaf project from an existing Git repository from this documentation.