How can I initiate use of my NEW password to go back to receiving emails on my phone??

What password did you change? Your Apple ID password→What to do after you change your Apple ID or password - Apple Support. But note that normally this is no longer required; you just have to log in with the new password when prompted.

If it was an email password you can go to Settings/Mail/Accounts, tap on the account and edit both incoming and outgoing passwords. But if the account is not a POP3 account (it will say what it is when you tap on the account) the easiest solution is delete the account, restart your phone, and add the account back.