Will migration from old macbook pro to new macbook pro overwrite new files already added to new macbook pro?

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If you use Migration Assistant and delete the current account, yes. For this reason, I'd suggest inhering your Time Machine backup on the new Mac (If your new Mac inherits your backup history - Apple Support) and restoring specific items to the correct new locations: Restore items backed up with Time Machine on Mac - Apple Support.

If you do not have a Time Machine backup, you should create one on your old Mac so files can be restored to the new Mac. To start, you need an external hard drive. Here’s an excellent one sold by Apple: G-Technology 4TB G-DRIVE mobile USB-C Portable Hard Drive - Apple. You can then follow the steps in this Apple Support article to setup your Time Machine backup: Back up your Mac with Time Machine - Apple Support.

Jack