Define not connecting properly. Does it pick up signal?

Officially, that device isn’t on their approved list:

Yes, the phone picks up the signal and shows a 4G connection when mobile data is enabled, but there is no internet access. After 5–10 seconds, the network disconnects automatically and the issue repeats.

Was this phone bought from another network or is it SIM-free? I ask because if it came from a network like Vodafone it probably has a customised firmware variant that won’t work on iD Mobile. You can usually tell because a network splash screen is usually displayed when you first turn it on.

AI search result returns the following when searching using THREE UK as the network in use…
 

Based on user experiences, the ASUS ROG Phone 3 may experience issues with the Three UK network due to VoLTE (Voice over LTE) incompatibility or incorrect Access Point Name (APN) settings. Because Three has phased out its 3G network, a phone must support 4G/5G calling (VoLTE) to function properly. 

Here are the troubleshooting steps to resolve this, based on reported fixes:

1. Fix APN Settings (Data Connection)

If you have signal but no data, the APN settings may be incorrect. 

• Go to Settings > Network & Internet > Mobile Network > Access Point Names.
• Delete any existing APN profiles.
• Create a new APN with the following settings (often required for Three):
  • Name: Three
  • APN: three.co.uk
  • Username: (Leave blank)
  • Password: (Leave blank)
  • APN type:default,supl,mms
• Save, select this new APN, and restart your phone. 

2. Force VoLTE (Calling Issues)

If you cannot make or receive calls, your phone might be trying to use a non-existent 3G signal. 

• Try dialing *#*#3642623344#*#* in your dialer to enable VoLTE, though this may need to be repeated after a restart.
• Check Settings > Network & Internet > Call to see if VoLTE or "Wi-Fi Calling" options are available and enabled. 

3. Network & SIM Troubleshooting

• Move SIM Slot: Ensure your Three SIM is in Slot 1.
• Network Selection: Go to Settings > Network & Internet > Mobile Network > Network operators and set it to Automatic.
• Update Firmware: Ensure your ROG 3 is running the latest firmware, as updates can fix carrier compatibility issues.
• Toggle Airplane Mode:Turn it on for 10 seconds, then off to force a network refresh.
• Test with another SIM: If possible, try a non-Three SIM to rule out a broken SIM slot. 

If these steps do not work, it is possible the specific firmware version of your ROG Phone 3 is not fully compatible with Three UK's VoLTE requirements.

Disclaimer: Some of these suggestions are based on community troubleshooting for ROG Phone 3 and similar models (like ROG 7) facing issues in the UK. 

The phone was purchased in India and is SIM-free (unlocked). It was not bought from any UK network, and there is no network splash screen when the phone starts.