Read the article 'Two-factor authentication for Apple ID' (click here --> https://support.apple.com/HT204915 ) thoroughly. Various sections contain information that is key to you being able to set up and use a different telephone, Mac, iPad, or Watch to get a verification code you can use.
Read the sections about:
- Trusted phone numbers
- Manage your account. If you can still sign into your account, go to https://appleid.apple.com/ and add your new number, then sign out of iCloud and back in again on your devices.
- What if I can't access a trusted device or didn't receive a verification code?
And if necessary:
- If I can't sign in, how do I regain access to my account?
Get a verification code and sign in with two-factor authentication - https://support.apple.com/HT204974
Get a code from an Account Recovery Contact --> https://support.apple.com/HT212513