You need to set a “featured image” in the post that you are setting as sticky. You can set the featured image by going to the post > Edit and then scrolling all the way down until you see “Featured Image” on the right. If you don’t see it, go to “Screen Options” tab on top of the same screen next to “Help” and check on the required box. The featured image will replace the “Featured Post” area.
If you don’t want to set a featured image for the sticky post, you should try to create a twenty twelve child theme. The following link would get you started.
https://codex.www.ads-software.com/Child_Themes
If not then I will give you a trick for it, which is not the best way to do it but it might just serve your purpose for that particular post.
when you are on the edit post page, go to the “text” tab of your visual editor and paste the following code at the end of the post.
<style>
.featured-post { display: none; }
</style>
The above CSS will hide the div you don’t want. But you have to do this in every post you set as sticky.