Turn on both iPhones and connect them to Wi-Fi
Sign in to the same Apple ID on both devices if needed
Open Contacts on the old iPhone
Make sure Contacts sync is enabled in Settings > [your name] > iCloud > Contacts
On the new iPhone, sign in to the same Apple ID
Turn on Contacts sync in Settings > [your name] > iCloud > Contacts
Wait for the contacts to finish syncing
If using an iCloud backup, back up the old iPhone first
On the new iPhone, restore from the iCloud backup during setup
If using Quick Start, place both iPhones near each other and follow the setup prompts
If using a SIM card, move the SIM card to the new iPhone if the number is stored on it
If using Google or another account, add the account on the new iPhone and enable Contacts
If contacts do not appear, refresh Contacts by toggling sync off and on
Check that both devices are connected to the internet
Verify the contacts are saved in iCloud, not only on the old iPhone
Use AirDrop to share individual contacts if needed