For starting import of .ics feeds in some "automatic" way you need to configure the CRON script at the server.
Different servers, have the different interface in "server administration panel", that can contain menu about the CRON scripts.
The detail description about Linux style of CRON commands you can check here. But usually you can configure your cron script via your server administration panel, like ISP Manager or Cpanel, in more easy way via menu and not the commands. That's why better to contact support of your hosting about this point. Hosting support must to know exactly what server administration panel you are using at your server, and how to configure your CRON script.
You need to define the CRON command to access the page with your import .ics feeds shortcodes, during each 1 hour (or other reasonable period of time). So CRON script will access the page with import .ics feeds shortcodes in your website, and during these times, will be start of import process, from your other services.
Example of CRON command (for every 1 hour to run):
0 * * * * wget https://your-server.com/your-page-with-import/shortcodes