It sounds like you were using iCloud Photos, and that isn't really a backup service. iCloud Photos synchronizes pictures -- makes the Photos Libraries on all devices exactly the same as at iCloud.com. So if someone on one connected device erases pictures, then they are erased at iCloud.com and on all other connected devices. They actually go to Recently Deleted for a second chance, so if the other person didn't delete them from their Recently Deleted album, then you might find them there, either on you phone or at your account at iCloud.com. Have you looked at iCloud.com?
So, if your old iPhone was connected to your account, then you pretty much left the barn door open, and it doesn't help to close the door after all the horses have escaped. (Sorry-- it's the first time I've ever had a chance to use that old proverb!)
You can see this:
If you're missing photos or videos in the Photos app - Apple Support
Basically the above says to look in Recently Deleted and in Hidden. Unfortunately, if you don't keep your own backups to an external drive, then there really isn't any place else to look.
This may help next time:
What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support
