A website with articles has a preview function where only a small part of an article is displayed on the homepage. The user can click on a link to read the rest of the article. These links are labelled as read more, making it hard for screen reader users to know which topic they would read more about.

The best solution is to provide custom labels of such links with aria-label and aria-labelledby. This solution provides level AAA conformance.
Web Content Accessibility Guidelines relax the requirements for links: if the purpose of the link can be found on the same paragraph that the link is in, a level AA conformance can be achieved.