Getting a new
TN at the border means applying for TN status at the border and CBP issues an I-94 card. A change of employer is a TN petition filed with USCIS. You don't depart the U.S. during this process. You have to maintain employment with the first TN employer to be able to file with the second employer, and there is no H-1B portability: you cannot begin working for the new TN employer until the petition is approved. Unless you premium process, it will take months for USCIS approval.