If the layout of the app looks like the below then normally the default screen appears if the account has not correctly synced on the app.
To fix this please uninstall and reinstall the Arsenal app. Before logging back in, please log in and out of your account on Arsenal.com and also the online box office. Doing this should sync your data over and allow the digital pass icon to become available.
Please also ensure you are logged in with the email address that is associated to your membership.