Apple care

There is no means to purchase AppleCare+ past 60 days from purchase.

AppleCare Products - iPhone - Apple

How to buy

Purchase either AppleCare+ product with your new iPhone.

Or buy it within 60 days of your iPhone purchase:

• On your device (go to Settings > General > About and choose AppleCare+ Coverage Available)
• Online (requires you to verify your serial number and run a remote diagnostic)
• At an Apple Store (inspection of iPhone and proof of purchase are required)
• By calling 800-275-2273 (requires you to run a remote diagnostic and provide proof of purchase)

You can add AppleCare+ within 60 days of purchasing the phone. See→Buy an AppleCare plan - Apple Support