My older ipad not compatible with pandora. Can ipad software be updated beyond the current 9.3.5?

No.

Its internal hardware is too old, underpowered and completely incompatible with any current and future versions of iOS.

Sorry. It is what it is at this very late date.

If you need an iPad that can run the latest and greatest versions of iOS, as well as, the most current apps available, then, you will need to purchase a new iPad from Apple or a discounted, refurbished iPad from Apple’s Refurbished & Clearance section of Apple’s Website.

Best of Luck to You!

Settings>General>About>Model

What's listed there?

If your iPad is on iOS 9.3.5, it likely cannot be upgraded further. For a newer version of iOS, you'll need a newer iPad.

~Lyssa