compatibility HDMI stick with ATT Uverse cable

First... WiFi refers to internet.

Some U-Verse receivers are wireless. This isn't really "WiFi" but a different thing.

When you watch TV, it doesn't matter what other devices are on. Your U-Verse boxes (DVR and receivers) use a small bit of the internet bandwidth (download speed) but very little.

HDMI refers to the port/plug on the device. It's not necessarily a stick. You can have a DVD or Blu-ray player be HDMI. Your laptop can be HDMI.

But what you'll do is get a Roku, Chromecast, game system like a PS4, Xbox One or newer or even a laptop. You'll connect it via an HDMI cable (Roku, Chromecast and other streaming devices don't need the cable as it's all the same thing) to the HDMI port on your TV.

Usually this is something like "HDMI 2" or "HDMI 3."

The device may or may not be smart enough to flip it to that input on your TV.

From there, you may need to download the app onto the device.

Use the same username and password as you've been using.

From there, happy viewing!

Some devices like Roku or Chromecast may include a Disney+ button. Others don't. These buttons cannot be modified. Some Roku devices have two extra buttons that can be used for whatever you choose.

How can we add HDMI stick or else to be able to stream (in particular  Disney plus.)

Your U-verse TV DVR or Receiver is likely connected to your TV using an HDMI cable.  Assuming that you TV has another HDMI port, you'd connect your streaming device to your TV using that other HDMI port.  Then you can switch back and forth between inputs using your TV's remote control.

If your TV doesn't have two HDMI inputs, then you could either switch the cables at need, or get an HDMI switch.  They're little more expensive than an HDMI cable.

The streaming device can connect to your Internet Gateway using Wi-Fi, or an Ethernet cable if your streaming device supports that.

@Marilyn2w 

The gateway att supplies for your U-verse TV service has WiFi built in.  Your TV can have something like a Roku or FireTV plugged into it and can connect over WiFi to stream Disney+.  This has nothing to do with U-verse TV which is a separate product from att internet service.  

Thank you for that info.  I will check it out.