Hello! I understand that your newly installed Metronome: Tempo Lite app isn't producing any sound on your Apple Watch Series 3. Let's see if we can get that sorted out together.

To start, can I ask a couple of questions to better understand the situation?
- Is the app itself running on the Apple Watch, or is it playing sound through your iPhone instead?
- Have you checked the volume and mute/silent settings on your Apple Watch?
- Are you using any Bluetooth audio device (like AirPods) connected to your watch?

Meanwhile, I can suggest a few steps to try based on common sound issues on Apple Watch apps:

1. Check Silent Mode and Volume:
- On your Apple Watch, swipe up to open the Control Center and ensure Silent Mode (bell icon) is off.
- Then, check the volume by going to Settings > Sounds & Haptics and increasing the volume slider.

2. Confirm Audio Output:
- If you have Bluetooth headphones paired, the sound might be routed there. Try disconnecting Bluetooth devices temporarily to see if sound comes from the watch speaker.

3. Force Close and Relaunch the App:
- Press the side button, swipe to your Metronome Tempo Lite app, and swipe up to close it. Then reopen the app.

4. Restart Your Apple Watch:
- Hold the side button until the power off slider appears, then slide to power off. Wait a few seconds and power it back on.

5. Reinstall the App:
- On your iPhone, uninstall Metronome Tempo Lite and then reinstall it. This can clear up any installation issues.

6. Check for App and watchOS Updates:
- Make sure your Apple Watch is running the latest watchOS version (watchOS 7.x or later for Series 3).
- Also, check for any updates to the Metronome Tempo Lite app in the App Store.

Reportedly, the Metronome app for Apple Watch sometimes redirects sound output to your iPhone unless an audio device is connected to the watch itself4. This could explain why no sound is audible directly from the Watch speaker.

If after these steps the app is still silent directly from the watch speaker, one workaround is to connect Bluetooth headphones or speakers to your Watch, which should allow the metronome beats to be heard.

Could you try these and let me know if the sound returns or if you notice any different behavior? We can then dig deeper if necessary.