Transfer it to the vault and any character can access it.
But may I suggest you level up a character from scratch first? There's a lot of info/characters/locations that will help you understand The Taken King story later. Save the crystal for a second character to save grinding through it all over again so he/she can go straight to level 25 and start TTK.
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omgggg i was thinking about this because i don't need to rush. c: thank you!
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If you've got a couple of friends with the game to form a fireteam you'll get through it quicker because you'll be able to play each level at a higher difficulty. Don't forget to stop talking and listen to the cut scenes! And you're right... there's no rush. Destiny 2 expected September 2016. Welcome to the wilderness, Guardian!