Can I transfer old iphone content to a new iphone after setup?

You’ll need to restore it and set it up again, to transfer data automatically via iCloud backup or Quick start.

Otherwise you could manually attempt to move data. Cloud synced items can be automatically downloaded by signing in to the relevant cloud service.

You can from an iCloud backup or a computer backup but you will need to erase the new iPhone first. See instructions in Use iCloud to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support or Use iCloud to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

To erase your device, tap Settings > General > Reset > Erase All Content and Settings. This erases all data on your device. After you erase it, your device restarts and the "Hello" screen appears.