I am changing carriers old carrier iPhone 11 64gb and new carrier iPhone 13 256gb can I use quick start to transfer everything including photos videos etc

Setting up your new iPhone with your content and data is not dependent on your choice of carrier.

Follow the instructions in the Quick Start page linked at the head of this page. You will find this is the first step - after turning on your device - in Apple's instructions Set up your iPhone or iPad - Apple Support.

Yesterday I set up an iPad for a family member. This is being used away from home instead of the other option - a MacBook Pro. I used Quick Start to transfer all the settings and all the iCloud content such as iCloud Photos, contacts, calendars and so on. For this device I went no further because very few apps were wanted. I manually sought only a selection of apps from the App Store account, but as you can see in the set up support document you can proceed from the Quick Start stage to then load all your apps and data from a backup. Apple calls this a restore.

Yes you can use Quick Start to transfer data from old iPhone to your new iPhone.

Transfer Data from old iPhone to new-

Do you have a backup created either on iCloud or on your computer?

Method 1 - Backup your old iPhone on your computer like this 👉 How to back up your iPhone, iPad, and iPod touch - Apple Support and then Restore your new iPhone from that backup like this 👉 Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Method 2 - The Quick Start method and here is how to do that 👉 Use Quick Start to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

Axel F.

You are welcome.

Axel F.