Let’s Encrypt expects you to prove control over the exact name you want a certificate for. So, the easiest way to arrange this for your subdomain will usually be to run the Certbot software (or whichever client you’ve chosen) on the server which serves that subdomain itself.
Let’s Encrypt also follows redirects. I believe you should be able to set a redirect on the sub-domain to point to the main server. This should also allow you to create a single certificate for both names, if you wish.
That’s the most common way to achieve your goal here. One way or another Let’s Encrypt will want to achieve confidence that whoever wants this certificate is controlling the exact name requested. When they run from the named machine Certbot itself and other clients like acme.sh can usually easily arrange all that automatically. If it’s not possible to run such a client, there are other approaches, but you’d probably need to explain in more detail what’s going on so that people can suggest how to solve your specific problems.
Thanks for your answer. I am not sure where I would redirect to, as the subdomain is already pointing to the IP address on the on other server. I can see what you are saying, but not sure how to implement it
best
Nick