iMessages (blue bubbles) are sent via your data connection.
This can be either WiFi or your carrier’s data connection.
Check your Settings -> Mobile -> Mobile Data to ensure that it’s set to your new SIM.
Also, you’ll need to de-register your “old” number … and register your “new” number in iMessaging.
Deregister iMessage on your iPhone or online - Apple Support
Then:
Settings -> Apple ID (Your Name) -> Name, Phone Numbers, Email.
Press Edit, add your new phone number if it has not already been registered.
After, go to:
Settings -> Messages. Activate iMessage and check that your new number is in the Send & Receive menu.
If all this appears correct, you’ll likely need to contact your new carrier to sort-out your mobile data issues.