Native transfer methods are all or nothing - so you’ll either need to accept that the transfer from the old iPad will replace everything - or accept some pain in manually moving files, data and photos from one to the other.
You might consider manually saving anything that’s from your new iPad elsewhere - and then use available transfer methods to move the bulk from old to new, then copy the new data back across from wherever it was saved. Either way, you’ll need to establish the sequence that offers least pain.
Don’t forget, you have iCloud and/or iTunes/Finder on your PC or Mac computer to help with moving or backing-up data.
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
When you are ready, the best procedure for preparing you old device for disposal or reuse can be found here:
What to do before you sell, give away or trade in your iPhone, iPad or iPod touch – Apple Support