The Starz app, while it allows you to download to the phone, it does not allow for moving to or downloading to an SD card. This is to prevent people from making copies and transferring them elsewhere. Most services that allow for downloads to the phone do not allow for downloading to the SD card or moving to other devices.
In regard to moving apps to the SD card, you may be able to do so since your phone is rooted. However I would suggest posting the question about moving apps over in the "Rooting, Jailbreaking & Unlocking" Forum...
http/www.tomsguide.com/forum/forum-117.html
NOTE: They won't be able to help you move Starz downloads to the SD card, as stated above, this is a limitation put in by the service.
If the device was not rooted, you would need to be running Android "Marshmallow" or above to convert the SD card into "Internal" storage, which would then allow for running apps from it. I am including those instructions below.
First, you need to be using a phone that is running at least Android "Marshmallow" or be able to upgrade to it. Second, you will need the instructions I am including below. And third, you need a phone that has not been restricted by the manufacturer from making this change. Which does happen.
NOTE: If any of the steps are missing on your phone, or they don't work for you, then you have a phone that either has an older Android version or has been restricted by the manufacturer.
How to turn the "External" SD card into "Internal" storage on "Marshmallow".
NOTE: Please be sure you start with a blank SD card. It needs to be blank because when the card is converted to "Internal" storage, it will be formatted (wiped) and encoded (making the cards data only readable by that device).
1. Go to device “Settings”, then select “Storage”.
2. Select your "SD Card", then tap the “three-dot menu“ (top-right), now select “Settings” from in there.
3. Now select “Format as internal”, and then “Erase & Format”.
4. Your SD Card will now be formatted as internal storage.
5. Reboot your phone.
NOTE: If you don't reboot the phone, many things may not work correctly, so make sure you do.
How to turn the "External" SD card into "Internal" storage on "Nougat".
IMPORTANT NOTE: Be sure you start with a blank SD card. When the card is converted to "Internal" storage, it will be formatted (wiped) and encoded (making the cards data only readable by that device), so anything on it prior would be gone.
1. Go to "Settings", and then select "Storage & USB".
2. At the bottom of the list you should see the SD card's details, including the option to format it and make it "Internal" storage.
3. Once this is done, reboot the device and you can start running things from the card.
If you don't reboot the phone, some things may not work correctly, so make sure you do the reboot.