How do I get my phone to download apps when I am signed into my new iCloud account

“New iCloud account”? Why would you do that? That would look like you’re a different person. This new Apple ID does not own any of the previous Apple ID’s apps, books, music, etc. It doesn’t own any contacts, calendars, notes, etc.

how can I download app for my new iPhone 13???

I already type my apple account and it doesn't let my download my old app's

"Old apps" may no longer be supported. An app must be currently available in the App Store or you cannot use it.