Good and unusual question we don't see here much.
I've never swapped processors without also changing the motherboard, rebuilding from the ground up, and reinstalling Windows.
My guess would be that you don't have to do anything---assuming the new CPU is in fact fully compatible with the version of Windows that you are currently using. Just swap it out and remount the CPU cooler with fresh paste.
Might be a good idea to reset the BIOS to defaults?
Let others comment.