There is SCEP (https://en.m.wikipedia.org/wiki/Simple_Certificate_Enrollmen...) which allows that and is often found on network devices. You need a PKI which exposes a SCEP endpoint (ejbca or dogtag supports this). That the certificate is used as certificate for the HTTPS is up to the device implementation of the scep client or something else in the client though.

On servers, certmonger can do scep iirc. On private infrastructure, FreeIPA provides a packaged dogtag and you can create your own certificate profiles. Clients enrolled in freeipa have certmonger installed to refresh certificates.