Sign the new device into the same Apple Account you used before, install Reps, and open it. Your classes, subjects, cards and review schedule arrive on their own through iCloud. There is nothing to export and no account to log into.
Give it a few minutes on a good connection the first time. A library with a lot of photos and drawings takes longer to arrive than the card text does, so you may see your cards appear before their images do.
Open Reps on it one last time while it is online. That pushes anything you did recently but had not yet synced. It costs ten seconds and removes the only real risk here.
Study streaks and focus totals are kept per device, so the new phone starts its own count. Cards, schedules, classes and deadlines all transfer normally.
Check that iCloud Drive is on and that Reps is allowed to use it, then see the troubleshooting steps for cards not appearing across devices.
More answers on the help page, or write to [email protected].