Lnk.Bio offers the possibility to automatically pull your latest YouTube video and feature it in your Lnk.Bio page.
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To enable this feature, navigate to the Style, decide where you want to place the video, and click Add block.

In the modal window that opens, select Video and then switch to the Auto tab, and finally click on Log in with YouTube as shown below:

After you log in with YouTube, you will be prompted to choose your YouTube channel, and finally the latest video will appear.
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Nothing else to do: from this moment onwards, every time you publish a new video on your YouTube channel, it will automatically reflect on your Lnk.Bio profile