is it possible to change battery on iPad Pro A1584?

Maybe not through Apple.

You own a nearly 8-year old, 2015 1st generation iPad Pro.

That year and model iPad just went Vintage status since this old an iPad Pro will no longer recieve full OS upgrades/updates, any longer, from Apple and will be forever stuck to some version of iPadOS 16.

Most actual Apple Store locations will NOT actual repair or replace batteries in iPads and, to expedite speedy customet service, will ONLY offer in/out of warranty iPad replacement.

Your issue is that this 8-year old, 1st gen iPad Pro maybe too old for Apple or any Apple Stores to have replacement iPads to replace for the battery replacement service.

In this event, you will need to do online reseatch for a third party Apple product ceftified/qualified repair center that has expertise in actually repairing iPads ( many thrid party Apple mobile device repair centers can do various types of repairs inside of iPhones, but not so much for iPads ).

Some questioms you may ask of any found third party Apple product repair centers is whether, or not, the repair center has expertise in micro-soldering and in actually repairing BOTH iPhones AND iPads.

Be dilligent and buyer beware.

Sorry & Best of Luck to You!

Go to this web site for information about how to request battery service for your iPad: iPad Repair & Service - Apple Support

For cost and availability, enter your model information in the "Get an estimate" box at the bottom. (I will let you do this since what it will show will depend upon the country where you are located.)

Is it really time to change your battery? See this excerpt from: Batteries - Maximizing Performance - Apple

"A normal battery is designed to retain up to 80% of its original capacity at 500 complete charge cycles when operating under normal conditions. The one-year warranty includes service coverage for a defective battery. If it is out of warranty, Apple offers battery service for a charge."