When you say permanently deleted video.. was this recent? Did you remove it from the Recently Deleted album?
Check in the Photos app for the Recently Deleted album
If it's not there, the only way you'd be able to recover it would be if you have a backup that contains the video you are trying to recover. If you have such a backup, then you'd restore your phone with that backup.
Some things to keep in mind..
- If you restore your iPhone from a backup, you're basically putting it back to the state that it was in when the backup was made. So you can lose content between now and when the backup was made.
- If you use iCloud to sync your photos/videos, then an iPhone backup will not contain your photos/videos
- When you make an iPhone backup, it replaces the previous backup (unless you make a point of archiving it using a computer)
About backups for iPhone, iPad, and iPod touch - Apple Support
Locate backups of your iPhone, iPad, and iPod touch - Apple Support
Restore your iPhone, iPad, or iPod touch from a backup - Apple Support