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Official documentation and announcement: https://www.clearos.com/resources/documentation/clearos/content:en_us:7_ug_lets_encrypt
Install from web interface (in the System section), like all the other apps.
yum install app-lets-encrypt
System > Security > Let's Encrypt > Add
Primary Domain: example.org
Other Domains: www.example.org
System > Security > Let's Encrypt
Server > Web > Web Server > Add or Edit > Settings > Options > Digital Certificate
System -> General Settings > Settings > SSL Certificate -> Edit -> Pick Let's Encrypt certificate
It is quite easy to use Let's Encrypt certificates in other apps using the following document: https://www.clearos.com/resources/documentation/clearos/content:en_us:kb_howtos_using_letsencrypt_certificates_for_mail
Although primarily written for mail apps, the methodology should be easily extensible to other apps such as LDAP, the FTP server and OpenFire.