Some mail providers offer a Web Key Directory for their users to publish OpenPGP public keys. This is sometimes amended by the Web Key Service, which offers users an easy and confirmed method to publish and update their OpenPGP public keys in the provider's WKD.
KMail can already handle most of the mail handshake but there's to my knowledge no way to initiate the process from within KMail. Thunderbird's Enigmail extension supports the initial mail and this adds the same feature in a similar manner to Kleopatra, utilising GnuPG and Akonadi to create and send the mail required to initiate the WKS key publishing process.
It adds another File and context menu entry for Export to Provider, utilising the same icon as "Export to Server", which should be reviewed for following GUI guidelines. Also, new messages added should be reviewed for proper language.