In order to clone a git repository including all branches and tags you need to use two parameters when cloning the old and pushing to the new repository respectively:

git clone --bare http://example.com/old-repo.git
cd old-repo
git push --mirror http://example.com/new-repo.git

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Of course, the URLs to your repository might look different depending on the protocol used, username required, etc.
For a user git using the git protocol, it could be git@example.com:repository-namespace/repository.git