If your old OneDrive account is with another organisation, then I would suspect they would not allow for privacy / security reasons you to gain access to your files.
If the old OndDrive account is with your existing organisation, I would get their MS 365 Admin / Technical team to allow you access to migrate to the new account.
Either way the easiest way to migrate files from one account to another is to add the old account details (once enabled) in the OneDrive client and then you will have two OneDrive entries in File Explorer. Perforn a File Sync on the old OneDrive account and once completed, copy the files over to the new OneDrive account.
If I have misunderstood, please accept my apologies.