Here is one idea - use VLC Remote app (not tested):

• in your old Android device, install free VLC Player app
• in your new Android device, install VLC Remote app
• pair VLC Remote with the VLC instance in the old device
• connect old device to TV through HDMI
• manually run VLC player app in the old device
• remotely control VLC player from the new device

Let us know if this worked :)

Here is another app that is supposedly compatible with GingerBread:

ISL Light for Android

Access any Android phone or tablet remotely from your desktop computer or from another mobile device.

Supported Platforms

• 2.3 Gingerbread
• 3.x Honeycomb
• 4.0 Ice Cream Sandwich
• 4.x Jelly Bean
• 4.4 Kit Kat
• 5.x Lollipop

Also, VNC is one of the most popular cross-platform Remote Screen Sharing / Remote desktop protocols, so I just have googled "VNC Server for Android" and I've seen 2 apps but they both need ROOT access (on your old Android). Need to google "VNC Server for Android without rooting" or so

The idea is simple:

• VNC Server on your old Android
• VNC Client on your new Android or your Desktop PC - this setup will allow to control old Android device remotely

Here is an article that might be useful, they talk specifically as controlling another decice used as HDMI player, similar to what you want:

How to Use an Android Phone/Tablet to Control Another Android via Bluetooth

Link to Google Play, it does not need root

The Tablet Remote app

It uses Bluetooth to communicate with other Android device. Imagine a setup where you have an Android tablet connected to your HDTV via HDMI. In this setup, the tablet would serve as your media player. You need a remote control to use for your media player (i.e., your tablet) That’s where Tablet Remote comes into play. If you have a second Android device, you can use it as a remote control for managing your other device.

Here’s how it works:

1. Download the Tablet Remote app from the Android Market.
2. Install the app on your two Android devices.
3. The tablet connected to your HDTV will serve as the receiver, while your other device will serve as the controller.
4. Configure the receiver device by opening Setup in the Tablet Remote app. Then, enable the two options: “Enable tablet remote in the settings” and “Change the input method for tablet remote”.
5. Pair the two devices via Bluetooth. To do that, open the Connection screen in Tablet Remote. Tap on “Make device discoverable” and then tap on “Scan devices”. Make sure that Bluetooth is enabled on both devices, otherwise you will not be able to pair them.
6. You will see a list of detected Bluetooth devices. Select the other device from the list. Confirmation messages will appear on the other device. Follow the onscreen instructions to successfully pair the two devices.

7. Once the two devices are paired, you can now start controlling the receiver device. To do that, tap the Remote button on the controller device. You will be taken to a screen with playback control buttons that you can use for remotely controlling the receiver device.

   I would personally still prefer the universal solution i.e. the VNC Server / Client solution. With this app, UI looks somewhat limited:

.

.