Stopping BitLocker from prompting for the recovery key at startup

You need to disable Bitlocker and decrypt your drive. Then, you need need to take ownership of the new TPM and initialize it (this should happen during bitlocker setup). Finally, re-encrypt your drive.

Your drive is encrypted using a key that was stored in your old TPM. That key is not known by your new TPM. Doing this will encrypt your drive with a new key that will be stored in the new TPM, which will cause the prompts to cease.