Keeping Current On The Law: Citation Alerts

Users can "be advised when that author's existing works are cited by new articles. Simply click an author's name from search results, and click Set up e-mail alerts from the author's profile:"

Using Lexis' Shepard's® system, you can be alerted of any changes for a particular publication.
Navigate to the publication and select 'Other Citing Sources', followed by the bell icon above to create the alert.

For articles published on OUP's platform, Oxford Academic, users with an account may configure an article activity alert which allows one to receive an email showing citation count changes.
Navigate to the publication and there will be a box in the upper right hand side with a quick sign-up link for an article activity alert for that paper. Click to confirm your choice via a pop-up to 'Add Alerts'.

Scopus permits author and article citation alerts. For article citation alerts, from the document view, click on citation alert.

Web of Science permits article citation alerts, i.e. the service will alert you when an article cites a particular article. Click on "Saved Searches and Alerts" on the left menu.

Using Westlaw's KeyCite system, you can be alerted when new Citing References are added for a particular publication.
Navigate to the publication and select 'Citing References', followed by the bell icon to create the alert.