How can I grant qemu access to an image on an external HDD?

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If the external drive is EXT4, then you can do chcon -t virt_image_t /path/to/file.

If the drive is something else, it's more difficult. The other filesystems don't support permissions, so the default permissions are 644 and can't be modified. If you need to be able to write to the image, you will have to mount the drive with a different umask.