Hey there,
There are a lot of things to check about this problem let’s start:
If your contacts were synced from iCloud, then your new iPhone needs to have the same iCloud account as your old phone. If that is not the case, your contacts will not transfer to your new iPhone.
The first thing you will want to do is verify if you are using the same iCloud account as your old iPhone on your new iPhone. It’s pretty easy to do that and the following is how to do it.
On your iPhone, open the Settings app and tap on your name. It will open the iCloud settings screen. On the following screen, you will see your iCloud account. Make sure this ID and the one being used on your old iPhone is the same. If it is not, log-out and log-in using the ID that you had on your old iPhone and that should resolve the issue for you.
It could be that the contacts syncing option has been turned off on your new iPhone. If that’s the case, your iPhone won’t be able to get contacts from iCloud and thus you won’t have your old iPhone’s contacts on your new iPhone.
Ensure Contacts Option is Enabled in iCloud
iCloud allows you to select what content you wish to sync when the feature is enabled on your iPhone. If the contacts option is unchecked, your contacts will not sync to your new devices and so your old iPhone contacts will never get transferred over to your new iPhone.
It’s pretty easy to fix this issue. All you need to do is enable the contacts option in iCloud on your new iPhone and you will be good to go. To do that, open the Settings app and tap on your name. Tap on iCloud and turn the toggle for Contacts to the ON position.
Your new iPhone could be fetching contacts and their details from other sources such as Gmail and Yahoo if you have enabled those. To fix the issue, you may want to disable contacts from other service providers except for iCloud on your iPhone.
To do that, launch the Contacts app on your new iPhone > Tap on Groups at the top-left corner > Uncheck everything except for All iCloud option. It will make sure to only fetch contacts from your iCloud account and not any other service providers.
We will suffice to this point for the time being sure of the steps I sent you above. If you still need help, there will be other steps you can try, I will be waiting for your response.