Yes, your new employer would need to file a new O-1 petition with USCIS and if it were me, even though subsequent O-1 petitions are usually approved, I wouldn't

Yes, your new employer would need to file a new O-1 petition with USCIS and if it were me, even though subsequent O-1 petitions are usually approved, I wouldn't give notice until the petition is approved. Note however that the O-1 visa in your passport remains valid even if you change employers as long as there is an underlying approved petition through the new employer.