Setup cloudflare controlled subdomain

What is the name of the domain?

example.com

What is the error number?

none

What is the error message?

none

What is the issue you’re encountering

setting up a subdomain to be cloudflare controlled

What steps have you taken to resolve the issue?

I have setup a partial domain
Now i wish to create a cloudflare controlled subdomain

We have a working application on the main site for the business. We are now to create a second application from a subdomain.
I have been tasked with placing all from the subdomain behind a WAF.

I have setup the main domain using partial setup and need to move all that we have set up in the authorative domain to cloudflare, we have services using A records pointing at IPS and cnames pointing to thirdparty services.

Im lost as to how to set this up.
I presumed to set this up in cloudflare instead of the authoritative controller would be right but read i am wrong due to using partial setup.

we have as an example in the authoritative server

A >> *.internal.staging.newapp.example.com. >> 13.3.3.33
A >> *.staging.newapp.example.com. >> 33.143.223.33
CNAME >> thirdpartyapp.newapp.example.com. >> thirdpartyapp-cd-dlzdpvd1gmdyubdy.edge.tenants.uk.app.com.
CAME >> thirdpartyapp.staging.newapp.example.com. >> examplecom-staging-cd-nldcydjn8dtmodxd.edge.tenants.uk.app.com.