Nimbostratus
MVPrts What is the function of https://abc.com? Are you sending the client to https://apim-xyz.com/api to handle part of the client request and then the client is back to use https://abc.com? I'm not all that familiar with Azure APIM so I'm not aware of it's function in the client request. In regards to the client certificate, is that used as an authentication method for Azure APIM or are you referring to the SSL cert that the client uses to connect to the website? If it's for client authentication I'm not sure how you could handle this without the F5 acting as the proxy between the client and Azure APIM since a redirect just hands the client off to the next URL.
Nimbostratusabc.com has no function. It is a legacy URL.
Client doesn't return back to abc.com, everything is handled in APIM.
Certificate is used for authentication. I am not too familiar with F5, so any light you can shed on the redirect would be helpful. Or any information on how to achieve authentication in this case.
MVPrts If abc.com is legacy then you want to change your redirect to a 301 rather than a 307. Now in regards to client authentication, they would need a client certificate for both abc.com and apim-xyz.com in order for things to work after the redirect. Most likely the client certificate is for domain abc.com and since the destination is no longer abc.com they would need the one cert to cover both FQDNs or have two certs with each one having the name for the appropriate destination.