If you filed Change of Status to get your H1B, and your H1B approval comes with I-94 with same number as your TN I-94, and expires as your H1B expiration date, you dont have to activate your H1B.
If your H1B approval notice does not come with I-94, you might need to surrender your TN I-94 nex time leaving us, upon your return, you can get a new I-94 with H1B status.