The Update button is accessible on the Themes page.
The Update button only displays for active Pro or Plus Plan subscribers. If the button is absent, check your subscription on the Plans page.
Register theme button
If there is a Register theme button in place of the Update button, then the theme license needs to be linked via registration.
If the Update button is grey and inactive. This means that you reached the maximum for themes in your Online Store (20). Delete a theme to make room for the new, updated theme.