This could be because of any of the following reasons:
- Outlink code not integrated/integrated incorrectly - You need to follow the steps mentioned here to integrate Outlink with your site.
- Theme change - With theme change you need to re-integrate Outlink with your site (steps for integration).
- Outlink deactivated - You have toggled Activate 'Off' in the 'Edit Outlinks' screen. Activate 'On' and hit 'Save'.
In case the external link button is still not visible please contact us at firstname.lastname@example.org or raise a new support ticket.