Restoration of a iTunes or iCloud backup to an iOS/iPadOS device is all-or-nothing; selective restoration is not possible.
If your native Contacts App was not configured in iPad settings to synchronise with iCloud, your Contacts data will be included in your iCloud/iTunes backup. However, if Contacts in iCloud was previously enabled, your Contacts data will not be included in your backup - but will instead be stored in iCloud; in this situation, simply enabling Contacts iCloud will synchronise Contacts data with the device.
Settings > [Your Name / AppleID] > iCloud > Contacts - set to ON
These support pages should get you started with setup of your new iPad - and the methods of transferring your data from old to new iPad:
Set up your iPhone, iPad or iPod touch – Apple Support
Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support
Use Quick Start to transfer data to a new iPhone, iPad or iPod touch – Apple Support
If the donor iPad, from which you are transferring your data precedes iOS12.4, QuickStart will not be available.
“Transfer” is rather a misnomer. In reality, your data and setup is merely cloned to the new device. Nothing is moved or removed from the original device.
An alternative is to restore either an iCloud or iTunes backup to the new device:
How to back up your iPhone, iPad and iPod touch – Apple Support
Restore your iPhone, iPad, or iPod touch from a backup - Apple Support
Remember, data form core Apple Apps (e.g., Contacts, Calendars, Reminders, Notes, Messages etc.) that were previously synchronised with iCloud, will already be accessible when iCloud services are enabled on your new iPad.