Can I get pictures back that have been deleted for a year

From: If you're missing photos or videos in the Photos app - Apple Support

Anything in your Recently Deleted album stays there for 30 days. After 30 days, it's permanently deleted and you can't get it back.

If you were not using iCloud photos to sync your photographs, or you kept them in some otehr location, then they may still be stored on another device or as part of a backup. You can restore the backup ( Restore your iPhone, iPad, or iPod touch from a backup - Apple Support ) to recover the photos but doing this will require erasing your device and restoring everything back to the time when you made that backup.

If you're referring to recovery from the hard drive from which they were deleted originally the answer is no.

As pointed out by others if you possible have a backup of the library or original photos that are a year old then maybe.

With this in mind you might consider the this: get an external SSD and export all of the originals from your Photos library to it using the option to create folders based on Moments.

Then all new photos in the library export to folders and name the folder by date or event. Then, using Time Machine, backup both the boot drive and the external drive with the original photos.