Upvote:8
You won't have any issues, but you will need to get a new ESTA once you have your new passport.
To quote from the official source:
If you obtain a new passport or change your name, gender or country of citizenship, you will be required to apply for a new travel authorization. This is also required if one of your answers to any of the VWP eligibility questions changes. The associated fee of $14 will be charged for each new application.