When you are the 3rd party mail delivery service provider from your partner's perspective, if they want you to send emails on behalf of them for the domain XYZ123.com, you will need to setup CNAME delegation with them for DKIM to work.
You choose 2 x selector for the DKIM public key DNS records (usually 2, but can be more). Selector string is arbitrary, can be anything that uniquely identity you in their DNS records. For example if your company name is "MailHostABC", you can choose to use these two selector strings:
mailhostabc1
mailhostabc2
Then you generate the DKIM key pairs for both selectors, each selector requires one key pair. Generation can be done with many tools such as ssh-keygen, Putty or many online generators.
In your own domain's DNS records, create two TXT records like this (assuming your domain is mailhostabc.com)
selector1-XYZ123._domainkey.mailhostabc.com
selector2-XYZ123._domainkey.mailhostabc.com
The TXT value of both records will contain the public key of both DKIM key pairs respectively. For example the first record would have value like this:
"v=DKIM1; k=rsa; p=..."
(public key is appended after the "=" sign)
Here is a TXT value with mocked up public key:
"v=DKIM1; k=rsa; p=MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCehqKMB6znGXo/pC83mGObm8OWo4daBYBb9wqqDaflz7Mf9KW1oaUm9j7hQq7af7jha'jfasdjLJDSFJA;IOUERLKJW/QVHqYKlPX3hvYUohBxg//T0u0rK3OSJss3OrpkoRqd150ynYxwwLymsjIwODT7Gf9WZPcL86rdboSRm/ost4mwIDAQAB"
- With each DKIM key pairs, you keep the private key and configure it on your MTA host so that it can use the private key to sign emails.
You ask your partner (in this case your client) who manages the DNS records for XYZ123.com to add the following 2 x CNAME records that point to the TXT records created above
CNAME record 1: selector1._domainkey.XYZ123.com
points to: selector1-XYZ123._domainkey.mailhostabc.com
CNAME record 2: selector2._domainkey.XYZ123.com
points to: selector2-XYZ123._domainkey.mailhostabc.com
With this setup, there is no ongoing maintenance to be done at your partner's end. When you rotate the DKIM keys, you only need to update your MTA host and your TXT records with new private and public keys.
Regards.