I don't know if it might only have information you already know, but there's some information on upgrading certbot in this thread:
In general, there's not really a concept of "renewal" of a certificate from a protocol point of view. You can just request a new certificate that has the same list of domain names, and that's treated as a "renewal" for purposes of things like tracking rate limits. If you use a different client, then you probably need to update your web server's configuration accordingly to wherever the other client is saving the key & certificate.