Howdy Linda Sherman,
Thank you for posting to the Community. That is an excellent question. If you have the same operating system on the new tablet as the old one, then yes you will be able to transfer the app to the new tablet. If the operating system is different, then you will not be able to transfer it and will have to purchase the app on the new tablet. (Android>Android or iPad>iPad).
You will need to be logged into the original account, on the new tablet, that the SlingPlayer was purchased with. Once that is done, you can go to the app store and download from the "My Apps" Section for Android and the "Purchased" section on the iPad.
Hope this helps,
Sling Media Moderation Team