See the following Apple articles: If you've forgotten your Apple ID email address or phone number
If you've forgotten your Apple ID email address or phone number – Apple Support (UK)
Sign in to your Apple ID account page and edit / update your Apple ID details.
https://appleid.apple.com
-> edit your trusted new phone number.
This phone number is already in use with another account
Contact / visit your carrier.
You definitely have a contract with your carrier and ask if that phone number is assigned to you.
May be you have to deal with a 'cooling off period'.
It is possible that your new phone number is 'known' to Apple, may have been used/linked to another Apple ID.
Ask: what or which cooling-off period your carrier use.
An explanation of cooling-off period in my region:
There is a difference: by law there is no 'cooling off period'.
Vodafone writes in a response that original Vodafone numbers, ie numbers purchased by Vodafone from ACM (Authority for Consumers & Markets), will go back into circulation after approximately nine months; six months applies to T-Mobile. Hi and Tele2 are talking about three months. KPN indicates that there is no term, which means that 'a telephone number that becomes available today may possibly be issued again tomorrow'. The procedure after terminating a subscription is always the same, whether it concerns death or other reasons.