How do I reset Apple Account password without old phone number?

Per About trusted phone numbers and trusted devices for Apple Account - Apple Support

If you permanently don’t have access to either your trusted devices or your trusted phone number, you can still attempt to recover access to your account.

1. Try to sign in to your Apple Account.
2. Select “Didn’t Get a Code?” or “Can’t get to your devices?” on the verification code screen.
3. Choose “Can’t use [phone number]”.
4. If you don’t have access to any trusted phone number on file with your Apple Account, you can initiate the process to recover access to your account. Follow the onscreen steps.

When going thru the account recovery steps  you need to first enter in that old number to show you know it. Always scroll down for additional options in small blue print if the  ones showing don’t apply to/work for you. 

When starting the account recovery steps the credit card is an extra option and not required. (See prior tip)

t’s a two phase process, phase 1 is up to 72 hours. (People mistakenly think you’ll be able to reset after those 24-72 hours, but it actually says it’s evaluating and you’ll get an update. That update is phase 2, which can be a couple days or longer.

After the phase 1 wait check your email or go to https://iforgot.apple.com/  to see the phase 2 wait time.

On the recovery date and time if you don’t/can’t get the text/call/email just go back to https://iforgot.apple.com/ and it will allow you to finish the reset process, but don’t wait too long or might have to start account recovery again. Per How to use account recovery when you can’t reset your Apple Account password - Apple Support “When the waiting period is over”

During the wait period make sure you are carefully following the instructions for how you started recovery at https://support.apple.com/en-us/118574 or you will cancel the recovery process.