You have to finish the whole story line including killing Gaul. After credits finish and you go to new tower, go to gunsmith and he will have the gun. Seems you only get one NOT one per character as I did NOT get one when I finished the story with my second character.
English
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If you have already collected it from gunsmith it will be in your vault under collections. All characters have access to vault so they can grab it there.
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I did not finished the whole story yet So I do not have coldhearth
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That's why I am wondering if deleting my carried over Titan from Destiny 1 invalidated my ability to get Coldheart.
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Doubt it, I kept all three and got coldheart with a warlock as that was the First character to complete the story.