If you need to use your H1B visa to enter USA, you do need to carry both your old and new passports.
For the already filed applications/petitions, don't do anything.
To renew H1B/I-131/I-765, use the new passport number, and ATTACH a copy of all the information pages of the old passport, and the "Observations" page of your new passport.
For the already filed applications/petitions, don't do anything.
To renew H1B/I-131/I-765, use the new passport number, and ATTACH a copy of all the information pages of the old passport, and the "Observations" page of your new passport.