A theme you installed from GitHub doesn’t sit in the WordPress.org directory, so WordPress won’t show update notices for it on its own. There are 2 ways to stay current, depending on whether the theme helps you.
If the theme bundles an update checker
Some GitHub-hosted themes include a small update checker that watches the theme’s GitHub releases and surfaces an update notice in wp-admin, in the same place as any other theme update. You review it and update from there, and the new version is pulled from GitHub. Loupely Canvas works this way, so self-hosted installs get the same one-step update experience as a directory theme, without the directory.
If it doesn’t
Without a checker, updating is manual: download the new release zip, then either upload it over the old one or replace the theme folder in wp-content/themes. Back up first, and confirm the theme folder name stays the same so WordPress treats it as the same theme.
If a notice isn’t appearing
Confirm a newer release actually exists, allow for WordPress’s update check schedule rather than expecting it instantly, and make sure you installed the GitHub build rather than a directory edition. A WordPress.org listing of the same theme updates through the directory instead.
