If you would want to update both fetch and push URL, pointing to same repo
git remote set-url origin <new-repo-url>
Below command will set new repository as default repo to push only.
git remote set-url --push origin <new-repo-url>
If need to unset the Push URL setup by above command
git remote set-url --delete --push origin <current-push-URL>
solved How can I clone a GitHub repository, then push it to a new repository as origin?