I put the code in for my Upgraded Red Sparrow on my Xbox 360. I then launched Destiny, and was able to grab the Upgraded Red Sparrow from the shop. Later, when I launched Destiny on Xbox One, I can't access the Upgraded Red Sparrow. While hovering over the description for the Sparrow S-10V, it says in red "Requires Preorder Exclusive."
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The add on will need to be downloaded to ur ps4 or Xbox one to use it. So even though it is available on ur last gen console it is because the content was unlocked via the license on the console. Try renewing ur licenses on ur Xbox or ps4 and see if it becomes available to download from the add ons section of the store.