To access tabs offline, tap the heart icon in the top right corner to add the tab to your Favorites.
Note: You need to have an Ultimate Guitar account to be able to add tabs to Favorites. You can create an account in the Account section of the app.
I still can't access my Favorites offline
If you have a lot of favorites, you need to wait for them to fully load to access them offline.
If you re-login, reinstall the app, etc. your Favorites will need to be downloaded again.