If you have been tagged in an Instagram Story, and you would like to repost it to your own Story, follow these steps.
1) Tap the notifications icon in the upper right corner of your screen.
2) Select the message from the user who tagged you.
3) Tap "Add This to Your Story."
4) Edit the post however you'd like, then tap "next."
5) Choose either "share" to post to your Story, or "send" to send directly to another user.
Instagram does not currently allow reposting of Stories you are not tagged in, or Stories published by private accounts.