Welcome to Apple Support Communities.
I understand you want to recover photos that have been deleted from the "Recently Deleted Album". Here's a great article that explains what happens when you delete photos from that album.
Delete photos on your iPhone, iPad, and iPod touch
How do you backup your photos? If you have them saved elsewhere, then you could easily add it back to the phone.Delete photos permanently
If you want to permanently delete your photos or videos within 30 days, you can remove them from the Recently Deleted album. When you delete a photo from this album, you can't get it back.
- Open the Photos app and go to the Albums tab.
- Open the Recently Deleted album and tap Select.
- Tap each photo or video that you want to permanently delete.
- Tap Delete.
It's possible to recover older photos from a backup depending on certain criteria. This would depend on two things, one if the backup was created with those photos and two, you're not using iCloud Photo Library (If this is turned on, photos are not saved in the backups). Also, keep in mind that restoring from a backup will affect other data from your phone (Any information added after the backup was created won't be in the backup) especially when restoring from an older backup. Here are some links for more information about backups and how to do one:
About backups for iOS devices
Restore your iPhone, iPad, or iPod touch from a backup
Let me know if this helps.
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Cheers!