You can add a webhook on GitHub and have it point to our Pull Mirroring API [1], followed by manually setting up the integration to send status updates back [2].
We're looking to make this process easier, and have explored ways we might implement this in https://gitlab.com/gitlab-org/gitlab-ee/issues/5220.
[1] https://docs.gitlab.com/ee/api/projects.html#start-the-pull-...
[2] https://docs.gitlab.com/ee/user/project/integrations/github....