You can
- create a new private repository on github,
- then clone your current repository on github to your local machine,
- then add that new repository to one of the remote of the clone,
- and finally push it to the new repository.
For example, let say your current repository is git@github.com:me/current.git
and the new one is git@github.com:me/new.git
.
$ git clone git@github.com:me/current.git local-copy
$ cd local-copy
$ git remote add new-repo git@github.com:me/new.git
$ git push new-repo master
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