From your site I see that this typical link does not work:
http://staging7.reelingsilk.com/images/AMApx/gx_style11.jpg
but this link does work:
https://www.staging7.reelingsilk.com/academy/wp-content/uploads/2020/04/salute0005-200x133.jpg
From what Scrambler has suggested, you need to copy (move) the whole images/ directory into academy/wp-content/uploads/
That will make the image url something like:
https://www.staging7.reelingsilk.com/academy/wp-content/uploads/images/AMApx/gx_style11.jpg
Once a copy the images/directory is in the correct place, then using the Better Search Replace plugin, you will need to change the url portion reading reelingsilk.com/images/ to reelingsilk.com/academy/wp-content/uploads/images/
That will leave the start and end portions of the image urls unchanged. Only the directory locations will change.
Again, please TEST this and make a backup copy before you start, as undoing this may be a challenge, other than using the backup and starting again.
Regards!