Since iOS 17 you can tap save the subject as a sticker.
Once you have made a sticker , you can open a different image, then tap the button with the three sliders to open the adjustments tab, then open the markup tool.
In Markup tap the "+" button to add a sticker to the image, select the saved sticker and position ans scale it.
Now you have inserted your subject into a different image.
But this will not be possible on an older version of iOS. You will need at least iOS 17.
On a Mac with macOS 15 you can ctrl-click the subject on a photo and use the command to save the subject as a new photos. Then you can open the new photo in Preview and copy it and paste it with Preview onto another photo.