No - not automatically.
Any extra apps you’ve downloaded besides the ones that come pre-installed on every iPhone will only populate a new iPhone if the the old iPhone with your apps is backed up to either iCloud or your Mac — and during setup of the new iPhone, you set it up from that old iPhone’s backup.
But —
Your Apple ID remembers every app you’ve ever downloaded (and tossed), so if you sign into the App Store with your Apple ID then click on your name, then Purchased, it’ll display a list of every app you’ve ever downloaded.
From that list you could then download the ones you want for your new iPhone.