Transferring phone contacts is via SIM card and is not related to your data. To transfer from old iPad to new one, you need to restore it from a backup, or migrate it. There are different ways of accomplishing this. Read the below articles carefully.
Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch
https://support.apple.com/en-us/HT201269
Use Quick Start to transfer data to a new iPhone, iPad, or iPod touch
https://support.apple.com/en-us/HT210216
Before you start, make sure you make a fresh backup of your current device
How to back up your iPhone, iPad, and iPod touch
https://support.apple.com/en-us/HT203977