Can I replace the battery in an iPad Air?

You, on your own? No, not really.

Apple? Yes, they can replace the battery for a fee or for free if its still covered by warranty or you have Apple Care+

click here ➜ iPad Repair and Service - Apple Support

You can use the cost calculator a little down the page to get an estimate.

For practical purposes, for battery service of qualifying devices, Apple usually exchange the iPad for a renewed/refurbished iPad of the same model and specification. The cost of the exchange is the same as would otherwise be charged for battery replacement. When exchanged, the replacement iPad is yours to keep.

You can verify both eligibility and cost for your country/region here:

iPad Repair & Service - Apple Support

Exchanging the iPad is a quick and easy alternative - and if exchanged in store, is usually same day. Unlike iPhone, for which an in-store battery replacement might be possible, iPad’s must be sent to Apple’s service partner - this process taking potentially many weeks.