Generating CSR with existing private key

You can't generate private key with help of exiting CSR. I can suggest to choose below options.

Option 1: Generate new CSR and share to CERT provider and get cert.

Option 2: Check with Cert provider if they can consider exiting CSR(they have old csr) and share new Public Cert. Then replace exiting cert to new cert in F5.

Note: Take backup before making any changes for Options2