The answer is No. Once the data is overwritten, you can not recover it anymore.
Even if you delete the recording you can still get it back with third-party data recovery software, given that the deleted data is still stored in the sectors on the storage media but is invisible. Unfortunately, when the data such as image, documents, video, audio, etc., is overwritten, the new data occupy the space, and the old data is permanently erased, there is no way to recover them back.
Have you backed up the recording to your Mac, an external disk, or the iCloud drive, or sent it to others? You may try to find it from these places. You'd better back up the important files later to avoid the same situation.