Bitbucket, Github and other services tend to have a \"push\" hook, so that when you push code to the repository, the service can hit a url (possible on a production server),
The push event of a GitHub webhook allows for the repository server (GitHub) to contact repository clients (your servers in the cloud)
But if that doesn't work, you would have two approaches:
git pull
, followed by a git push
to a bare repo (still on the same cloud server): a post-receive hook on that bare repo can be triggered if the git push
pushed anything at all (As I mentioned in the comments of "How to execute a command right after a fetch or pull command in git?").