I'm guessing that you have a repo on your local machine.
Do you have the repo created at github?
You want to sync the two, I'm guessing that you need to do something like the following:
<url_of_old_repo> is the url to the repo where you created it on github
git clone --mirror <url_of_old_repo>
cd <name_of_old_repo>
git remote add new-origin <url_of_new_repo>
git push new-origin --mirror
If you have everything created (locally & remotely -- github) then you may just need to follow the last two steps.