Let’s pretend you have a project on Gitlab called ask-izzy and you want to mirror it up to Gitlab which is located at https://github.com/ask-izzy/ask-izzy
Assuming you’re running Gitlab as the default user of git and that your repositories are stored in /mnt/repositories you can following something similar to the following instructions:

Grant write access to Github

Get your Gitlab install’s pubkey from the git user
cat /home/git/.ssh/id_rsa.pub
On Github add this pubkey as deploy key on the repo, make sure you tick the option to allow write access.

Sam McLeod

Step-by-step guide to mirror a GitLab repository to GitHub using SSH deploy keys and a post-receive hook. Covers granting write access via a deploy key, creating a custom post-receive hook that auto-pushes to GitHub on every commit, and configuring GitHub as a remote with mirror mode in the GitLab repo's git config.

Mirroring a Gitlab project to Github