There is not any setting or short code attribute at the moment to hide the description. Unfortunately, our current version doesn't add any special CSS class name in the description element to hide even using CSS.
As an immediate solution, you can just edit our template files and remove the description, change the "Read More" button text or do whatever you need.
The files you will need to edit are,
/wp-content/plugins/another-events-calendar/public/partials/events/aec-public-events-blog-display.php
/wp-content/plugins/another-events-calendar/public/partials/events/aec-public-events-grid-display.php
/wp-content/plugins/another-events-calendar/public/partials/events/aec-public-events-map-display.php
/wp-content/plugins/another-events-calendar/public/partials/events/aec-public-events-table-display.php