Drywall, also known as plasterboard or gypsum, is mostly used in house or building construction. It's used to create flat walls to segment a house into rooms, due to its easy installation and effectiveness.
It was reported back in 2018 that around 7,500 tons of drywall is made every year in the US, with around 15% of that being waste. That accounts to a whopping 1125 tons of drywall wasted every year. This is a huge amount of waste considering drywall can actually be recycled and repurposed. Due to its composition and how it's made, drywall can be repurposed into brand new sheets of drywall easily.
Gypsum is a Calcium Sulfate dehydrate; it's used along with paper and water which is then kiln-fired into sheets of drywall.
Calcium Sulfate is a natural mineral but in its form of gypsum. Bacteria will convert the gypsum into hydrogen Sulfide. Hydrogen Sulfide is a poisonous gas and is considered toxic.
A large number of resources will tell you that Calcium Sulfate is good for your soil. However, in its gypsum form this just isn't true. This is why a large amount of gypsum board / drywall is actually used as soil amendments in agriculture. However, do we really want to be adding potentially toxic chemicals into our soil.
With this in mind, you will want to search a place that repurposes drywall specifically. They will be able to properly recycle the drywall, to be used in new drywall sheets. This will keep it out of landfill and from creating toxic gases in our agricultural farming.
It is not likely that you will be able to put drywall in your recycling bin. In fact most normal recycling centres won't be able to deal with drywall and won't even accept it. You are better off either trying to reuse the drywall yourself. Or if the sheets are big enough trying to find someone that can use them.
If the above suggestions aren't possible. Look for a recycling company that can remodel the drywall for use in new sheets of drywall.