Transferring photos and apps from iPhone 13 to iPhone 15

Use Quick Start to transfer data to a new iPhone or iPad – Apple Support (UK)

or

Turn on and set up iPhone - Apple Support

Apps cannot be transferred directly, they can be re-downloaded from the App Store assuming you are using the same Apple ID on the 15 as on the 13.

click here ➜ Redownload apps and games from Apple - Apple Support

For Photos, if you have already setup the iPhone, then you either need to setup iCloud Photos or airdrop the photos from one to the other.

click here ➜ Set up and use iCloud Photos - Apple Support

or here ➜ How to use AirDrop on your iPhone or iPad - Apple Support

If you have not set up the iPhone 15 yet, you can use Quick Start or Set up the 15 from a backup of the 13 to transfer everything from the old iPhone to the new one. In that process, Apps installed on the old iPhone will be setup to download from the App Store automatically to the new iPhone and photos will be transferred during the setup process.

click here ➜ Use Quick Start to transfer data to a new iPhone or iPad - Apple Support

or here ➜ Set up your iPhone or iPad - Apple Support