Thank you for using Apple Support Communities. It's my understanding that you're missing a years worth of photos after restoring from an old backup. I know photos can be very valuable. I'm happy to help.
If you were previously using iCloud Photo Library, it's possible your photos are still in iCloud. In this case the photos could be accessed by downloading from iCloud.com or turning on iCloud Photo Library. Please review the steps and information in the link below:
iCloud Photo Library
Have a wonderful day!