If we count the Disney Animal Kingdom Lodge as a separate AZA facility then they opened in 2001, but it is definitely not a traditional zoo.
New aquariums are more common than new zoos. Mote Marine should be opening their new large aquarium in a couple of months and they are AZA accredited. SEA LIFE Legoland Florida opened earlier this year and is not accredited yet, but the other SEA LIFE aquariums are, so it should be soon.
The new Wonders of Wildlife in Springfield opened in 2017. The original was 2001, but it was less than 50% the size of the current place. Shreveport Aquarium opened in 2017 and is not AZA yet but is in their Pathway program, for whatever that is worth.
I know the intention of the question is zoos in the USA portion of AZA, but Seaworld Abu Dhabi opened in 2023.
I don't think any new traditional zoos have been built since DAK that are AZA accredited. Some have lost their accreditation for several years and then regained it, but that isn't like building a new zoo to AZA specs.
The truth is that building a zoo from the ground up to AZA specs is not really possible for a private individual unless one is independently wealthy and just wants to blow a lot of cash on the project - a lot of cash, in the hundreds of millions of dollars. You might be able to open a very small zoo to AZA standards, but it likely could not draw enough to keep the doors open. Running a zoo is costly, and without money from outside sources it is likely an endeavor that will quickly fail. This is why most private zoos have side enterprises for breeding and sales to other private entities.
The small private places that make it are typically ran by the owner providing much of the hands on work along with relying on volunteers and a few low paid individuals looking for experience so that they can move to larger AZA zoos, so turn over can be high.
