For a domain’s cert prior to expiry (within 30 days though), the existing CSR can simply be submitted to the cert provider and payment made etc for renewal if one isn’t changing any cert details e.g. company name etc. Then simply install the new cert via WHM and, after testing, delete the old one (also through WHM, it will have had .old
For a server cert e.g. for imap, smtp, ftp etc, one can also use the old csr, but be sure to go into Service Configuration > Manage Service SSL Certificates and hit “install new certificate” for each service.