In EST a certificate issued by the EST server can be used as an HTTPS client certificate. This can be used to authorize the re-issue of the certificate. In OPC UA a certificate issued by the GDS can be used to establish a secure channel. This would then allow the GDS client to request that the certificate be re-issued.
In both EST and OPC UA clients can fall back to the authentication mechanisms used for Initial Enrolment if it is not possible to use the current certificate to establish a secure channel with the server.