Updating Exchange certificates

Federation Trusts

Federation makes free/busy times and on-prem calendar/contact sharing available through Exchange Online. Process to renew is different if the cert has already expired.
https://learn.microsoft.com/en-us/exchange/renew-the-federation-certificate-exchange-2013-help
https://social.technet.microsoft.com/Forums/en-US/c863b6c9-9456-47f2-a1e1-db1787acc83f/unable-to-publish-next-federation-certificate

Send/Receive Connectors

TlsCertificateName must be formatted like <I>issuer DN<S>subject name, e.g.:

$cert = Get-ExchangeCertificate -Thumbprint ABC123
$cert = "<I>$($cert.Issuer)<S>$($cert.Subject)"
Set-SendConnector "Outbound to Contoso" -TlsCertificateName $cert
Set-ReceiveConnector "Default Frontend Exchange" -TlsCertificateName $cert

https://www.azure365pro.com/replacing-send-connector-certificate/