Start manually the same actions that you usually do in your hook after taking, which is most important:
cd /path/to/website git pull
It is assumed that /path/to/website is a clone from your Git repository, and you configured its current branch to track the Git repository branch where you deploy your releases.
So, after you push your commits to the Git repository, you can update your website:
ssh yourserver 'cd /path/to/website; git pull'
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