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For troubleshooting on this, take a look at this article:
iPhone: Troubleshooting a cellular data connection
Follow the instructions below for assistance with troubleshooting cellular data issues on your iPhone. After performing each step, please test to see if the issue is resolved.
- Toggle cellular data off and then on again on the iPhone: Tap Settings > General > Cellular.
- Restart your iPhone.
- Check for a carrier settings update.
- Update your iPhone.
- Remove the SIM Card and reinsert it. Allow the iPhone to reaquire the network.
- If your SIM card has SIM PIN enabled, try toggling it off: Tap Settings > Phone > SIM PIN.
- Try another location. If a different location works, but the original location still does not, contact your carrier to report the issue.
- Reset network settings: Tap Settings > General > Reset > Reset Network Settings.
- Restore the iPhone as new.
- Contact your carrier to verify that the iPhone is properly set up on the account with the appropriate, current data plan. If you are traveling internationally, you may need to turn data roaming on: Tap Settings > General > Cellular. Check with your carrier first to understand the cost of international data roaming. Also, see this article.
Note: If your carrier does not appear in this list, verify with your carrier that you are using the correct cellular data settings.
Hope this helps,