Can I add warranty coverage to a new phone I just recieve?d

If this is a new iPhone 15 model or another model iPhone you bought new from Apple, yes. You have 60 days (not one day more) to add an AppleCare+ plan to the phone. See this link --> Buy an AppleCare plan - Apple Support

Your phone has a 1-year warranty.

You can purchase one of two “premium” warranty options within 60-days of initial purchase:

AppleCare Products - iPhone - Apple