This app was mentioned in 2 comments, with an average of 2.00 upvotes
PlayStation Video is in the Play Store.
PlayStation Vue is in the Play Store.
The only other Sony PS app is PlayStation Remote Play, but that will only officially work on Sony devices. You can try a hacked copy, but it will likely require a mouse/keyboard setup and will be difficult getting gamepad support on an Android TV device, most likely.
In the future, before posting here asking for APKs, why not try the Play Store or Google first?
Edit: I did snoop through my TV via adb and found the PlayStation Now apk file. I uploaded it to APKMirror, so check there in the near future to see if it's been approved by them and you'll be able to download it.
Edit 2: ApkMirror was taking too long, here's a direct link to the PS Now apk I pulled from my 2015 Bravia: http://www.filedropper.com/psnow
I believe they are separate stores now. did you try this app: https://play.google.com/store/apps/details?id=com.playstation.video