The process of re-keying a certificate involves creating a new certificate with a different public key (and serial number and key identifier) while retaining the remaining contents of the old certificate that describe the subject. 

Circumstances that warrant for a certificate re-key 

1. When the key is lost
2. When the key is compromised 
3. When the certificate is expired
4. When there is an issuance of a new token
5. When there is an enforcement of a standard or application

The Process to re-key a certificate is similar to that of issuance of a Digital Signing Certificate