when you get a new phone do the apps you previously paid for transfer to the new phone without purchasing again?

There is not need of worries about transferring the paid apps to the newer iPhone because whenever you purchase a app its registered to your apple id. There are two ways of transferring apps from old iPhone to new iPhone:

1. Sign in from same apple id that you were using on old iPhone. Go to the apple store and download apps that you already paid for, it will give you an option of restore purchase. There you can restore your purchase (which is 100% free) and download the app again.
2. Backup your old iPhone using either iCloud or iTunes (I use iTunes as it takes few minutes to completely backup my iPhone). On your new iPhone just simply restore your iPhone from the backup the you have previously taken. It will bring each and every app that you had on your old iPhone to your newer iPhone (Free as well as Paid).
3. Enjoy . .

I was simply trying to explain in clear, punctuated English, how to migrate to a new device. It was not intended to be an exhaustive exploration of every minor edge case. It also included accurate information of how to go about it.

On the new phone you simply log-in to the App Store using the same Apple ID, and all your previous purchases are there for you to download to the new device.

All free and purchased apps are connected to Yours Apple id,only in case if the app developer replaced the purchased app can charge again or ask to buy it again.

until the already purchased app haven been replaced by the app developer for other version bc that case You need to buy it again.and if You move using backup it will move also Your apps

https://support.apple.com/en-us/HT201269