Migration from Swipe-up to Link Stickers
From August 30 2021, Instagram gradually switched its users from the Swipe-up link to the Stories Link Sticker.
The new sticker behaves like the mention and hashtag stickers and can be placed anywhere on the story.
Only one Link Sticker can be added per story.
Link Stickers will be available to some users with less than 10k followers which have some kind of influence on Instagram.
2021-09-14 Facebook / Instagram is still working on fully implementing the link sticker. Even if you post a Facebook story via the Instagram app, the link sticker is not clickable on the Facebook website at the moment. They also still changing the link sticker design:

Yes! You can add Link Stickers like you would Hashtags or Mention stickers in our story editor
Link Stickers will only work if your Instagram account supports them
There are 3 different designs
You can only add one Link Sticker per Instagram story slide
You can add Link Stickers to your story via the Editor only at the moment.
Open a story in the editor
go to the sticker tab
click on the Link Sticker
Enter your url (starting with http:// or https://)
And (NEW) add an optional name to it. This name will be displayed to the story viewer, it should be linked to the address but is not sticking to it.
Here are some screenshots how the UI looks like:


The Bulk scheduling tool was a handy tool to add Swipe-Up links to scheduled stories.
If your account made the transition to Link Stickers, this functionality is lost.
Please don't insert links there if your account supports Link Stickers
We are planing to adapt this to Link Stickers soonish so that Stickers are automatically added to your story if you insert a link in the bulk scheduling tool.
The new sticker behaves like the mention and hashtag stickers and can be placed anywhere on the story.
Only one Link Sticker can be added per story.
Link Stickers will be available to some users with less than 10k followers which have some kind of influence on Instagram.
Important
2021-09-14 Facebook / Instagram is still working on fully implementing the link sticker. Even if you post a Facebook story via the Instagram app, the link sticker is not clickable on the Facebook website at the moment. They also still changing the link sticker design:

Does Storrito support the new Link Sticker?
Yes! You can add Link Stickers like you would Hashtags or Mention stickers in our story editor
Link Stickers will only work if your Instagram account supports them
There are 3 different designs
You can only add one Link Sticker per Instagram story slide
How to add a Link Sticker to my story?
You can add Link Stickers to your story via the Editor only at the moment.
Open a story in the editor
go to the sticker tab
click on the Link Sticker
Enter your url (starting with http:// or https://)
And (NEW) add an optional name to it. This name will be displayed to the story viewer, it should be linked to the address but is not sticking to it.
Here are some screenshots how the UI looks like:


Future work
The Bulk scheduling tool was a handy tool to add Swipe-Up links to scheduled stories.
If your account made the transition to Link Stickers, this functionality is lost.
Please don't insert links there if your account supports Link Stickers
We are planing to adapt this to Link Stickers soonish so that Stickers are automatically added to your story if you insert a link in the bulk scheduling tool.
Updated on: 11/01/2023
Thank you!